Joint L1 and total variation regularization for fluorescence molecular tomography

Logarithmic total variation regularization via preconditioned conjugate gradient method for sparse reconstruction of bioluminescence tomography

BACKGROUND AND OBJECTIVE

Bioluminescence Tomography (BLT) is a powerful optical molecular imaging technique that enables the noninvasive investigation of dynamic biological phenomena. It aims to reconstruct the three-dimensional spatial distribution of bioluminescent sources from optical measurements collected on the surface of the imaged object. However, BLT reconstruction is a challenging ill-posed problem due to the scattering effect of light and the limitations in detecting surface photons, which makes it difficult for existing methods to achieve satisfactory reconstruction results. In this study, we propose a novel method for sparse reconstruction of BLT based on a preconditioned conjugate gradient with logarithmic total variation regularization (PCG-logTV).

METHOD

This PCG-logTV method incorporates the sparsity of overlapping groups and enhances the sparse structure of these groups using logarithmic functions, which can preserve edge features and achieve more stable reconstruction results in BLT. To accelerate the convergence of the algorithm solution, we use the preconditioned conjugate gradient iteration method on the objective function and obtain the reconstruction results. We demonstrate the performance of our proposed method through numerical simulations and in vivo experiment.

RESULTS AND CONCLUSIONS

The results show that the PCG-logTV method obtains the most accurate reconstruction results, and the minimum position error (LE) is 0.254mm, which is 26%, 31% and 34% of the FISTA (0.961), IVTCG (0.81) and L1-TV (0.739) methods, and the root mean square error (RMSE) and relative intensity error (RIE) are the smallest, indicating that it is closest to the real light source. In addition, compared with the other three methods, the PCG-logTV method also has the highest DICE similarity coefficient, which is 0.928, which means that this method can effectively reconstruct the three-dimensional spatial distribution of bioluminescent light sources, has higher resolution and robustness, and is beneficial to the preclinical and clinical studies of BLT.

Difference of Convex Functions Programming With Machine-Learning Prior for the Imaging Problem in Electrical Capacitance Tomography

The electrical capacitance tomography technology has potential benefits for the process industry by providing visualization of material distributions. One of the main technical gaps and impediments that must be overcome is the low-quality tomogram. To address this problem, this study introduces the data-guided prior and combines it with the electrical measurement mechanism and the sparsity prior to produce a new difference of convex functions programming problem that turns the image reconstruction problem into an optimization problem. The data-guided prior is learned from a provided dataset and captures the details of imaging targets since it is a specific image. A new numerical scheme that allows a complex optimization problem to be split into a few less difficult subproblems is developed to solve the challenging difference of convex functions programming problem. A new dimensionality reduction method is developed and combined with the relevance vector machine to generate a new learning engine for the forecast of the data-guided prior. The new imaging method fuses multisource information and unifies data-guided and measurement physics modeling paradigms. Performance evaluation results have validated that the new method successfully works on a series of test tasks with higher reconstruction quality and lower noise sensitivity than the popular imaging methods.

Adaptive Sparsity Orthogonal Least Square with Neighbor Strategy for Fluorescence Molecular Tomography

Fluorescence molecular tomography (FMT) is a highly sensitive and noninvasive optical imaging technique which has been widely applied to disease diagnosis and drug discovery. However, FMT reconstruction is a highly ill-posed problem. In this work, L0-norm regularization is employed to construct the mathematical model of the inverse problem of FMT. And an adaptive sparsity orthogonal least square with a neighbor strategy (ASOLS-NS) is proposed to solve this model. This algorithm can provide an adaptive sparsity and can establish the candidate sets by a novel neighbor expansion strategy for the orthogonal least square (OLS) algorithm. Numerical simulation experiments have shown that the ASOLS-NS improves the reconstruction of images, especially for the double targets reconstruction.Clinical relevance- The purpose of this work is to improve the reconstruction results of FMT. Current experiments are focused on simulation experiments, and the proposed algorithm will be applied to the clinical tumor detection in the future.

Reconstruction based on adaptive group least angle regression for fluorescence molecular tomography

Fluorescence molecular tomography can combine two-dimensional fluorescence imaging with anatomical information to reconstruct three-dimensional images of tumors. Reconstruction based on traditional regularization with tumor sparsity priors does not take into account that tumor cells form clusters, so it performs poorly when multiple light sources are used. Here we describe reconstruction based on an "adaptive group least angle regression elastic net" (AGLEN) method, in which local spatial structure correlation and group sparsity are integrated with elastic net regularization, followed by least angle regression. The AGLEN method works iteratively using the residual vector and a median smoothing strategy in order to adaptively obtain a robust local optimum. The method was verified using numerical simulations as well as imaging of mice bearing liver or melanoma tumors. AGLEN reconstruction performed better than state-of-the-art methods with different sizes of light sources at different distances from the sample and in the presence of Gaussian noise at 5-25%. In addition, AGLEN-based reconstruction accurately imaged tumor expression of cell death ligand-1, which can guide immunotherapy.

Stopping-power ratio estimation for proton radiotherapy using dual-energy computed tomography and prior-image constrained denoising

BACKGROUND

Dual-energy computed tomography (DECT) is a promising technique for estimating stopping-power ratio (SPR) for proton therapy planning. It is known, however, that deriving electron density (ED) and effective atomic number (EAN) from DECT data can cause noise amplification in the resulting SPR images. This can negate the benefits of DECT.

PURPOSE

This work introduces a new algorithm for estimating SPR from DECT with noise suppression, using a pair of CT scans with spectral separation. The method is demonstrated using phantom measurements.

MATERIALS AND METHODS

An iterative algorithm is presented, reconstructing ED and EAN with noise suppression, based on Prior Image Constrained Denoising (PIC-D). The algorithm is tested using a Siemens Definition AS+ CT scanner (Siemens Healthcare, Forchheim, Germany). Three phantoms are investigated: a calibration phantom (CIRS 062M), a QA phantom (CATPHAN 700), and an anthropomorphic head phantom (CIRS 731-HN). A task-transfer function (TTF) and the noise power spectrum are derived from SPR images of the QA phantom for the evaluation of image quality. Comparisons of accuracy and noise for ED, EAN, and SPR are made for various versions of the algorithm in comparison to a solution based on Siemens syngo.via Rho/Z software and the current clinical standard of a single-energy CT stoichiometric calibration. A gamma analysis is also applied to the SPR images of the head phantom and water-equivalent distance (WED) is evaluated in a treatment planning system for a proton treatment field.

RESULTS

The algorithm is effective at suppressing noise in both ED and EAN and hence also SPR. The noise is tunable to a level equivalent to or lower than that of the syngo.via Rho/Z software. The spatial resolution (10% and 50% frequencies in the TTF) does not degrade even for the highest noise suppression investigated, although the average spatial frequency of noise does decrease. The PIC-D algorithm showed better accuracy than syngo.via Rho/Z for low density materials. In the calibration phantom, it was superior even when excluding lung substitutes, with root-mean-square deviations for ED and EAN less than 0.3% and 2%, respectively, compared to 0.5% and 3%. In the head phantom, however, the SPR accuracy of the PIC-D algorithm was comparable (excluding sinus tissue) to that derived from syngo.via Rho/Z: less than 1% error for soft tissue, brain, and trabecular bone substitutes and 5-7% for cortical bone, with the larger error for the latter likely related to the phantom geometry. Gamma evaluation showed that PIC-D can suppress noise in a patient-like geometry without introducing substantial errors in SPR. The absolute pass rates were almost identical for PIC-D and syngo.via Rho/Z. In the WED evaluations no general differences were shown.

CONCLUSIONS

The PIC-D DECT algorithm provides scanner-specific calibration and tunable noise suppression. It is vendor agnostic and applicable to any pair of CT scans with spectral separation. Improved accuracy to current methods was not clearly demonstrated for the complex geometry of a head phantom, but the suppression of noise without spatial resolution degradation and the possibility of incorporating constraints on image properties, suggests the usefulness of the approach.

D2-RecST: Dual-domain joint reconstruction strategy for fluorescence molecular tomography based on image domain and perception domain

BACKGROUND AND OBJECTIVE

Fluorescence molecular tomography (FMT) is a promising molecular imaging modality for quantifying the three-dimensional (3D) distribution of fluorescent probes in small animals. Over the past few years, learning-based FMT reconstruction methods have achieved promising results. However, these methods typically attempt to minimize the mean-squared error (MSE) between the reconstructed image and the ground truth. Although signal-to-noise ratios (SNRs) are improved, they are susceptible to non-uniform artifacts and loss of structural detail, making it extremely challenging to obtain accurate and robust FMT reconstructions under noisy measurements.

METHODS

We propose a novel dual-domain joint strategy based on the image domain and perception domain for accurate and robust FMT reconstruction. First, we formulate an explicit adversarial learning strategy in the image domain, which greatly facilitates training and optimization through two enhanced networks to improve anti-noise ability. Besides, we introduce a novel transfer learning strategy in the perceptual domain to optimize edge details by providing perceptual priors for fluorescent targets. Collectively, the proposed dual-domain joint reconstruction strategy can significantly eliminate the non-uniform artifacts and effectively preserve the structural edge details.

RESULTS

Both numerical simulations and in vivo mouse experiments demonstrate that the proposed method markedly outperforms traditional and cutting-edge methods in terms of positioning accuracy, image contrast, robustness, and target morphological recovery.

CONCLUSIONS

The proposed method achieves the best reconstruction performance and has great potential to facilitate precise localization and 3D visualization of tumors in in vivo animal experiments.

Tikhonov regularization-based extended Kalman filter technique for robust and accurate reconstruction in diffuse optical tomography

Diffuse optical tomography (DOT) is a non-invasive imaging modality that uses near-infrared light to probe the optical properties of tissue. In conventionally used deterministic methods for DOT inversion, the measurement errors were not taken into account, resulting in unsatisfactory noise robustness and, consequently, affecting the DOT image reconstruction quality. In order to overcome this defect, an extended Kalman filter (EKF)-based DOT reconstruction algorithm was introduced first, which improved the reconstruction results by incorporating a priori information and measurement errors to the model. Further, to mitigate the instability caused by the ill-condition of the observation matrix in the tomographic imaging problem, a new, to the best of our knowledge, estimation algorithm was derived by incorporating Tikhonov regularization to the EKF method. To verify the effectiveness of the EKF algorithm and Tikhonov regularization-based EKF algorithm for DOT imaging, a series of numerical simulations and phantom experiments were conducted, and the experimental results were quantitatively evaluated and compared with two conventionally used deterministic methods involving the algebraic reconstruction technique and Levenberg-Marquardt algorithm. The results show that the two EKF-based algorithms can accurately estimate the location and size of the target, and the imaging accuracy and noise robustness are obviously improved. Furthermore, the Tikhonov regularization-based EKF obtained optimal parameter estimations, especially under the circumstance of low absorption contrast (1.2) and high noise level (10%).

Excitation-based fully connected network for precise NIR-II fluorescence molecular tomography

Fluorescence molecular tomography (FMT) is a novel imaging modality to obtain fluorescence biomarkers' three-dimensional (3D) distribution. However, the simplified mathematical model and complicated inverse problem limit it to achieving precise results. In this study, the second near-infrared (NIR-II) fluorescence imaging was adopted to mitigate tissue scattering and reduce noise interference. An excitation-based fully connected network was proposed to model the inverse process of NIR-II photon propagation and directly obtain the 3D distribution of the light source. An excitation block was embedded in the network allowing it to autonomously pay more attention to neurons related to the light source. The barycenter error was added to the loss function to improve the localization accuracy of the light source. Both numerical simulation and in vivo experiments showed the superiority of the novel NIR-II FMT reconstruction strategy over the baseline methods. This strategy was expected to facilitate the application of machine learning in biomedical research.

Reconstruction of fluorophore absorption and fluorescence lifetime using early photon mesoscopic fluorescence molecular tomography: a phantom study

SIGNIFICANCE

Fluorescence molecular lifetime tomography (FMLT) plays an increasingly important role in experimental oncology. The article presents and experimentally verifies an original method of mesoscopic time domain FMLT, based on an asymptotic approximation to the fluorescence source function, which is valid for early arriving photons.

AIM

The aim was to justify the efficiency of the method by experimental scanning and reconstruction of a phantom with a fluorophore. The experimental facility included the TCSPC system, the pulsed supercontinuum Fianium laser, and a three-channel fiber probe. Phantom scanning was done in mesoscopic regime for three-dimensional (3D) reflectance geometry.

APPROACH

The sensitivity functions were simulated with a Monte Carlo method. A compressed-sensing-like reconstruction algorithm was used to solve the inverse problem for the fluorescence parameter distribution function, which included the fluorophore absorption coefficient and fluorescence lifetime distributions. The distributions were separated directly in the time domain with the QR-factorization least square method.

RESULTS

3D tomograms of fluorescence parameters were obtained and analyzed using two strategies for the formation of measurement data arrays and sensitivity matrices. An algorithm is developed for the flexible choice of optimal strategy in view of attaining better reconstruction quality. Variants on how to improve the method are proposed, specifically, through stepped extraction and further use of a posteriori information about the object.

CONCLUSIONS

Even if measurement data are limited, the proposed method is capable of giving adequate reconstructions but their quality depends on available a priori (or a posteriori) information. Further research aims to improve the method by implementing the variants proposed.

Multi-branch attention prior based parameterized generative adversarial network for fast and accurate limited-projection reconstruction in fluorescence molecular tomography

Limited-projection fluorescence molecular tomography (FMT) allows rapid reconstruction of the three-dimensional (3D) distribution of fluorescent targets within a shorter data acquisition time. However, the limited-projection FMT is severely ill-posed and ill-conditioned due to insufficient fluorescence measurements and the strong scattering properties of photons in biological tissues. Previously, regularization-based methods, combined with the sparse distribution of fluorescent sources, have been commonly used to alleviate the severe ill-posed nature of the limited-projection FMT. Due to the complex iterative computations, time-consuming solution procedures, and less stable reconstruction results, the limited-projection FMT remains an intractable challenge for achieving fast and accurate reconstructions. In this work, we completely discard the previous iterative solving-based reconstruction themes and propose multi-branch attention prior based parameterized generative adversarial network (MAP-PGAN) to achieve fast and accurate limited-projection FMT reconstruction. Firstly, the multi-branch attention can provide parameterized weighted sparse prior information for fluorescent sources, enabling MAP-PGAN to effectively mitigate the ill-posedness and significantly improve the reconstruction accuracy of limited-projection FMT. Secondly, since the end-to-end direct reconstruction strategy is adopted, the complex iterative computation process in traditional regularization algorithms can be avoided, thus greatly accelerating the 3D visualization process. The numerical simulation results show that the proposed MAP-PGAN method outperforms the state-of-the-art methods in terms of localization accuracy and morphological recovery. Meanwhile, the reconstruction time is only about 0.18s, which is about 100 to 1000 times faster than the conventional iteration-based regularization algorithms. The reconstruction results from the physical phantoms and in vivo experiments further demonstrate the feasibility and practicality of the MAP-PGAN method in achieving fast and accurate limited-projection FMT reconstruction.

A review of advances in imaging methodology in fluorescence molecular tomography

Objective. Fluorescence molecular tomography (FMT) is a promising non-invasive optical molecular imaging technology with strong specificity and sensitivity that has great potential for preclinical and clinical studies in tumor diagnosis, drug development and therapeutic evaluation. However, the strong scattering of photons and insufficient surface measurements make it very challenging to improve the quality of FMT image reconstruction and its practical application for early tumor detection. Therefore, continuous efforts have been made to explore more effective approaches or solutions in the pursuit of high-quality FMT reconstructions. Approach. This review takes a comprehensive overview of advances in imaging methodology for FMT, mainly focusing on two critical issues in FMT reconstructions: improving the accuracy of solving the forward physical model and mitigating the ill-posed nature of the inverse problem from a methodological point of view. More importantly, numerous impressive and practical strategies and methods for improving the quality of FMT reconstruction are summarized. Notably, deep learning methods are discussed in detail to illustrate their advantages in promoting the imaging performance of FMT thanks to large datasets, the emergence of optimized algorithms and the application of innovative networks. Main results. The results demonstrate that the imaging quality of FMT can be effectively promoted by improving the accuracy of optical parameter modeling, combined with prior knowledge, and reducing dimensionality. In addition, the traditional regularization-based methods and deep neural network-based methods, especially end-to-end deep networks, can enormously alleviate the ill-posedness of the inverse problem and improve the quality of FMT image reconstruction. Significance. This review aims to illustrate a variety of effective and practical methods for the reconstruction of FMT images that may benefit future research. Furthermore, it may provide some valuable research ideas and directions for FMT in the future, and could promote, to a certain extent, the development of FMT and other methods of optical tomography.

Multispectral interlaced sparse sampling photoacoustic tomography based on directional total variation

BACKGROUND AND OBJECTIVE

Photoacoustic tomography (PAT) is capable of obtaining cross-sectional images of small animals that represent the optical absorption of biological tissues. The multispectral Interlaced Sparse Sampling PAT, or ISS-PAT, is a previously proposed PAT imaging method that offered high quality images with much sparser transducer angular coverage. Although it provides superior imaging performance, the original ISS-PAT method suffered from a heavy computation burden, which hinders its practical application.

METHODS

Here, we propose a new regularization scheme based on the directional total variation (dTV) for ISS-PAT. This method efficiently imposes the structural information by considering both the edge position and direction information of the anatomical prior image in ISS-PAT. It does not require image segmentation, and can be conveniently solved by a modified alternating direction of multipliers (ADMM) algorithm.

RESULTS

We perform simulation, tissue mimicking phantom and in vivo small animal experiments to evaluate the proposed scheme. The reconstructed PAT images showed image quality and spectral un-mixing accuracy close to those obtained by non-local means based ISS-PAT, but with much shorter image reconstruction time. For a 1/6 sparse sampling rate, the average efficiency improvement is nearly 16-folds.

CONCLUSIONS

The experimental results demonstrate the feasibility of the dTV regularization scheme for ISS-PAT. Its efficient image reconstruction performance facilitates the potential of the hardware realization and practical applications of the ISS-PAT.

End-To-End Bioluminescence Tomography Reconstruction Based On Convolution Neural Network Scheme

Bioluminescence tomography (BLT) has received a lot of attention as an important technique in bio-optical imaging. Compared with traditional methods, neural network methods have the advantages of fast reconstruction speed and support for batch processing. In this paper, we propose a end-to-end BLT reconstruction based on convolution neural networks scheme. First, 3000 datasets with single source and dual sources projection were conducted by Monte Carlo method, respectively. And three convolution neural networks (VGGNet, ResNet, and DenseNet) were adopted to feature extraction. Then, the filtered features were used as input to the multi-layer perceptron (MLP) to predict the source location. The results of numerical simulation and simulation experiments show, compared with traditional methods, the advantages of our method are including high reconstruction accuracy, faster reconstruction, few parameters, simple reconstruction process and support for batch processing.

UHR-DeepFMT: Ultra-High Spatial Resolution Reconstruction of Fluorescence Molecular Tomography Based on 3-D Fusion Dual-Sampling Deep Neural Network

Fluorescence molecular tomography (FMT) is a promising and high sensitivity imaging modality that can reconstruct the three-dimensional (3D) distribution of interior fluorescent sources. However, the spatial resolution of FMT has encountered an insurmountable bottleneck and cannot be substantially improved, due to the simplified forward model and the severely ill-posed inverse problem. In this work, a 3D fusion dual-sampling convolutional neural network, namely UHR-DeepFMT, was proposed to achieve ultra-high spatial resolution reconstruction of FMT. Under this framework, the UHR-DeepFMT does not need to explicitly solve the FMT forward and inverse problems. Instead, it directly establishes an end-to-end mapping model to reconstruct the fluorescent sources, which can enormously eliminate the modeling errors. Besides, a novel fusion mechanism that integrates the dual-sampling strategy and the squeeze-and-excitation (SE) module is introduced into the skip connection of UHR-DeepFMT, which can significantly improve the spatial resolution by greatly alleviating the ill-posedness of the inverse problem. To evaluate the performance of UHR-DeepFMT network model, numerical simulations, physical phantom and in vivo experiments were conducted. The results demonstrated that the proposed UHR-DeepFMT can outperform the cutting-edge methods and achieve ultra-high spatial resolution reconstruction of FMT with the powerful ability to distinguish adjacent targets with a minimal edge-to-edge distance (EED) of 0.5 mm. It is assumed that this research is a significant improvement for FMT in terms of spatial resolution and overall imaging quality, which could promote the precise diagnosis and preclinical application of small animals in the future.

Correntropy-induced metric with Laplacian kernel for robust fluorescence molecular tomography

Fluorescence molecular tomography (FMT), which is used to visualize the three-dimensional distribution of fluorescence probe in small animals via the reconstruction method, has become a promising imaging technique in preclinical research. However, the classical reconstruction criterion is formulated based on the squared l ₂-norm distance metric, leaving it prone to being influenced by the presence of outliers. In this study, we propose a robust distance based on the correntropy-induced metric with a Laplacian kernel (CIML). The proposed metric satisfies the conditions of distance metric function and contains first and higher order moments of samples. Moreover, we demonstrate important properties of the proposed metric such as nonnegativity, nonconvexity, and boundedness, and analyze its robustness from the perspective of M-estimation. The proposed metric includes and extends the traditional metrics such as l ₀-norm and l ₁-norm metrics by setting an appropriate parameter. We show that, in reconstruction, the metric is a sparsity-promoting penalty. To reduce the negative effects of noise and outliers, a novel robust reconstruction framework is presented with the proposed correntropy-based metric. The proposed CIML model retains the advantages of the traditional model and promotes robustness. However, the nonconvexity of the proposed metric renders the CIML model difficult to optimize. Furthermore, an effective iterative algorithm for the CIML model is designed, and we present a theoretical analysis of its ability to converge. Numerical simulation and in vivo mouse experiments were conducted to evaluate the CIML method's performance. The experimental results show that the proposed method achieved more accurate fluorescent target reconstruction than the state-of-the-art methods in most cases, which illustrates the feasibility and robustness of the CIML method.

A Novel Adaptive Parameter Search Elastic Net Method for Fluorescent Molecular Tomography

Fluorescence molecular tomography (FMT) is a new type of medical imaging technology that can quantitatively reconstruct the three-dimensional distribution of fluorescent probes in vivo. Traditional Lp norm regularization techniques used in FMT reconstruction often face problems such as over-sparseness, over-smoothness, spatial discontinuity, and poor robustness. To address these problems, this paper proposes an adaptive parameter search elastic net (APSEN) method that is based on elastic net regularization, using weight parameters to combine the L1 and L2 norms. For the selection of elastic net weight parameters, this approach introduces the L0 norm of valid reconstruction results and the L2 norm of the residual vector, which are used to adjust the weight parameters adaptively. To verify the proposed method, a series of numerical simulation experiments were performed using digital mice with tumors as experimental subjects, and in vivo experiments of liver tumors were also conducted. The results showed that, compared with the state-of-the-art methods with different light source sizes or distances, Gaussian noise of 5%-25%, and the brute-force parameter search method, the APSEN method has better location accuracy, spatial resolution, fluorescence yield recovery ability, morphological characteristics, and robustness. Furthermore, the in vivo experiments demonstrated the applicability of APSEN for FMT.

Early-photon reflectance fluorescence molecular tomography for small animal imaging: Mathematical model and numerical experiment

The paper presents an original approach to time-domain reflectance fluorescence molecular tomography (FMT) of small animals. It is based on the use of early arriving photons and state-of-the-art compressed-sensing-like reconstruction algorithms and aims to improve the spatial resolution of fluorescent images. We deduce the fundamental equation that models the imaging operator and derive analytical representations for the sensitivity functions which are responsible for the reconstruction of the fluorophore absorption coefficient. The idea of fluorescence lifetime tomography with our approach is also discussed. We conduct a numerical experiment on 3D reconstruction of box phantoms with spherical fluorescent inclusions of small diameters. For modeling measurement data and constructing the sensitivity matrix we assume a virtual fluorescence tomograph with a scanning fiber probe that illuminates and collects light in reflectance geometry. It provides for large source-receiver separations which correspond to the macroscopic regime. Two compressed-sensing-like reconstruction algorithms are used to solve the inverse problem. These are the algebraic reconstruction technique with total variation regularization and our modification of the fast iterative shrinkage-thresholding algorithm. Results of our numerical experiment show that our approach is capable of achieving as good spatial resolution as 0.2 mm and even better at depths to 9 mm inclusive.

K-Nearest Neighbor Based Locally Connected Network for Fast Morphological Reconstruction in Fluorescence Molecular Tomography

Fluorescence molecular tomography (FMT) is a highly sensitive and noninvasive imaging modality for three-dimensional visualization of fluorescence probe distribution in small animals. However, the simplified photon propagation model and ill-posed inverse problem limit the improvement of FMT reconstruction. In this work, we proposed a novel K-nearest neighbor based locally connected (KNN-LC) network to improve the performance of morphological reconstruction in FMT. It directly builds the inverse process of photon transmission by learning the mapping relation between the surface photon intensity and the distribution of fluorescent source. KNN-LC network cascades a fully connected (FC) sub-network with a locally connected (LC) sub-network, where the FC part provides a coarse reconstruction result and LC part fine-tunes the morphological quality of reconstructed result. To assess the performance of our proposed network, we implemented both numerical simulation and in vivo studies. Furthermore, split Bregman-resolved total variation (SBRTV) regularization method and inverse problem simulation (IPS) method were utilized as baselines in all comparisons. The results demonstrated that KNN-LC network achieved accurate reconstruction in both source localization and morphology recovery in a short time. This promoted the in vivo application of FMT for visualizing the distribution of biomarkers inside biological tissue.

Development of tomographic reconstruction for three-dimensional optical imaging: From the inversion of light propagation to artificial intelligence

Optical molecular tomography (OMT) is an imaging modality which uses an optical signal, especially near-infrared light, to reconstruct the three-dimensional information of the light source in biological tissue. With the advantages of being low-cost, noninvasive and having high sensitivity, OMT has been applied in preclinical and clinical research. However, due to its serious ill-posedness and ill-condition, the solution of OMT requires heavy data analysis and the reconstruction quality is limited. Recently, the artificial intelligence (commonly known as AI)-based methods have been proposed to provide a different tool to solve the OMT problem. In this paper, we review the progress on OMT algorithms, from conventional methods to AI-based methods, and we also give a prospective towards future developments in this domain.

NIR-II/NIR-I Fluorescence Molecular Tomography of Heterogeneous Mice Based on Gaussian Weighted Neighborhood Fused Lasso Method

Fluorescence molecular tomography (FMT), which can visualize the distribution of fluorescence biomarkers, has become a novel three-dimensional noninvasive imaging technique for in vivo studies such as tumor detection and lymph node location. However, it remains a challenging problem to achieve satisfactory reconstruction performance of conventional FMT in the first near-infrared window (NIR-I, 700-900nm) because of the severe scattering of NIR-I light. In this study, a promising FMT method for heterogeneous mice was proposed to improve the reconstruction accuracy using the second near-infrared window (NIR-II, 1000-1700nm), where the light scattering significantly reduced compared with NIR-I. The optical properties of NIR-II were analyzed to construct the forward model for NIR-II FMT. Furthermore, to raise the accuracy of solution of the inverse problem, we proposed a novel Gaussian weighted neighborhood fused Lasso (GWNFL) method. Numerical simulation was performed to demonstrate the outperformance of GWNFL compared with other algorithms. Besides, a novel NIR-II/NIR-I dual-modality FMT system was developed to contrast the in vivo reconstruction performance between NIR-II FMT and NIR-I FMT. To compare the reconstruction performance of NIR-II FMT with traditional NIR-I FMT, numerical simulations and in vivo experiments were conducted. Both the simulation and in vivo results showed that NIR-II FMT outperformed NIR-I FMT in terms of location accuracy and spatial overlap index. It is believed that this study could promote the development and biomedical application of NIR-II FMT in the future.

Low Dose CT Image Reconstruction Based on Structure Tensor Total Variation Using Accelerated Fast Iterative Shrinkage Thresholding Algorithm

Low dose computed tomography (CT) has drawn much attention in the medical imaging field because of its ability to reduce the radiation dose. Recently, statistical iterative reconstruction (SIR) with total variation (TV) penalty has been developed to low dose CT image reconstruction. Nevertheless, the TV penalty has the drawback of creating blocky effects in the reconstructed images. To overcome the limitations of TV, in this paper we firstly introduce the structure tensor total variation (STV₁) penalty into SIR framework for low dose CT image reconstruction. Then, an accelerated fast iterative shrinkage thresholding algorithm (AFISTA) is developed to minimize the objective function. The proposed AFISTA reconstruction algorithm was evaluated using numerical simulated low dose projection based on two CT images and realistic low dose projection data of a sheep lung CT perfusion. The experimental results demonstrated that our proposed STV₁-based algorithm outperform FBP and TV-based algorithm in terms of removing noise and restraining blocky effects.

Reconstruction for Fluorescence Molecular Tomography via Adaptive Group Orthogonal Matching Pursuit

OBJECTIVE

Fluorescence molecular tomography (FMT) is a promising medical imaging technology aimed at the non-invasive, specific, and sensitive detection of the distribution of fluorophore. Conventional sparsity prior-based methods of FMT commonly face problems such as over-sparseness, spatial discontinuity, and poor robustness, due to the neglect of the interrelation within the local subspace. To address this, we propose an adaptive group orthogonal matching pursuit (AGOMP) method.

METHODS

AGOMP is based on a novel local spatial-structured sparse regularization, which leverages local spatial interrelations as group sparsity without the hard prior of the tumor region. The adaptive grouped subspace matching pursuit method was adopted to enhance the interrelatedness of elements within a group, which alleviates the over-sparsity problem to some extent and improves the accuracy, robustness, and morphological similarity of FMT reconstruction. A series of numerical simulation experiments, based on digital mouse with both one and several tumors, were conducted, as well as in vivo mouse experiments.

RESULTS

The results demonstrated that the proposed AGOMP method achieved better location accuracy, fluorescent yield reconstruction, relative sparsity, and morphology than state-of-the-art methods under complex conditions for levels of Gaussian noise ranging from 5-25%. Furthermore, the in vivo mouse experiments demonstrated the practical application of FMT with AGOMP.

CONCLUSION

The proposed AGOMP can improve the accuracy and robustness for FMT reconstruction in biomedical application.

Adaptive Gaussian Weighted Laplace Prior Regularization Enables Accurate Morphological Reconstruction in Fluorescence Molecular Tomography

Fluorescence molecular tomography (FMT), as a powerful imaging technique in preclinical research, can offer the three-dimensional distribution of biomarkers by detecting the fluorescently labelled probe noninvasively. However, because of the light scattering effect and the ill-pose of inverse problem, it is challenging to develop an efficient reconstruction method, which can provide accurate location and morphology of the fluorescence distribution. In this research, we proposed a novel adaptive Gaussian weighted Laplace prior (AGWLP) regularization method, which assumed the variance of fluorescence intensity between any two voxels had a non-linear correlation with their Gaussian distance. It utilized an adaptive Gaussian kernel parameter strategy to achieve accurate morphological reconstructions in FMT. To evaluate the performance of the AGWLP method, we conducted numerical simulation and in vivo experiments. The results were compared with fast iterative shrinkage (FIS) thresholding method, split Bregman-resolved TV (SBRTV) regularization method, and Gaussian weighted Laplace prior (GWLP) regularization method. We validated in vivo imaging results against planar fluorescence images of frozen sections. The results demonstrated that the AGWLP method achieved superior performance in both location and shape recovery of fluorescence distribution. This enabled FMT more suitable and practical for in vivo visualization of biomarkers.

Regularized reconstruction based on joint L1 and total variation for sparse-view cone-beam X-ray luminescence computed tomography

As an emerging hybrid imaging modality, cone-beam X-ray luminescence computed tomography (CB-XLCT) has been proposed based on the development of X-ray excitable nanoparticles. Owing to the high degree of absorption and scattering of light through tissues, the CB-XLCT inverse problem is inherently ill-conditioned. Appropriate priors or regularizations are needed to facilitate reconstruction and to restrict the search space to a specific solution set. Typically, the goal of CB-XLCT reconstruction is to get the distributions of nanophosphors in the imaging object. Considering that the distributions of nanophosphors inside bodies preferentially accumulate in specific areas of interest, the reconstruction of XLCT images is usually sparse with some locally smoothed high-intensity regions. Therefore, a combination of the L₁ and total variation regularization is designed to improve the imaging quality of CB-XLCT in this study. The L₁ regularization is used for enforcing the sparsity of the reconstructed images and the total variation regularization is used for maintaining the local smoothness of the reconstructed image. The implementation of this method can be divided into two parts. First, the reconstruction image was reconstructed based on the fast iterative shrinkage-thresholding (FISTA) algorithm, then the reconstruction image was minimized by the gradient descent method. Numerical simulations and phantom experiments indicate that compared with the traditional ART, ADAPTIK and FISTA methods, the proposed method demonstrates its advantage in improving spatial resolution and reducing imaging time.

Reconstruction of Fluorescence Molecular Tomography via a Fused LASSO Method Based on Group Sparsity Prior

OBJECTIVE

The aim of this paper is to improve the reconstruction accuracy in both position and source region of fluorescence molecular tomography (FMT).

METHODS

The reconstruction of the FMT is challenging due to its serious ill-posedness and ill-condition. Currently, to obtain the fluorescent sources accurately, more a priori information of the fluorescent sources is utilized and more efficient and practical methods are proposed. In this paper, we took the group sparsity of the fluorescent sources as a new type of priori information in the FMT, and proposed the fused LASSO method (FLM) for FMT. The FLM based on group sparsity prior not only takes advantage of the sparsity of the fluorescent sources, but also utilizes the structure of the sources, thus making the reconstruction results more accuracy and morphologically similar to the sources. To further improve the reconstruction efficiency, we adopt Nesterov's method to solve the FLM.

RESULTS

Both heterogeneous numerical simulation experiments and in vivo mouse experiments were carried out to verify the property of the FLM. The results have verified the superiority of the FLM over conventional methods in tumor detection and tumor morphological reconstruction. Furthermore, the in vivo experiments had demonstrated that the FLM has great potential in preclinical application of the FMT.

SIGNIFICANCE

The reconstruction method based on group sparsity prior has a great potential in the FMT study, it can further improve the reconstruction quality, which has practical significance in preclinical research.

Recent methodology advances in fluorescence molecular tomography

Molecular imaging (MI) is a novel imaging discipline that has been continuously developed in recent years. It combines biochemistry, multimodal imaging, biomathematics, bioinformatics, cell & molecular physiology, biophysics, and pharmacology, and it provides a new technology platform for the early diagnosis and quantitative analysis of diseases, treatment monitoring and evaluation, and the development of comprehensive physiology. Fluorescence Molecular Tomography (FMT) is a type of optical imaging modality in MI that captures the three-dimensional distribution of fluorescence within a biological tissue generated by a specific molecule of fluorescent material within a biological tissue. Compared with other optical molecular imaging methods, FMT has the characteristics of high sensitivity, low cost, and safety and reliability. It has become the research frontier and research hotspot of optical molecular imaging technology. This paper took an overview of the recent methodology advances in FMT, mainly focused on the photon propagation model of FMT based on the radiative transfer equation (RTE), and the reconstruction problem solution consist of forward problem and inverse problem. We introduce the detailed technologies utilized in reconstruction of FMT. Finally, the challenges in FMT were discussed. This survey aims at summarizing current research hotspots in methodology of FMT, from which future research may benefit.

Image reconstruction in fluorescence molecular tomography with sparsity-initialized maximum-likelihood expectation maximization

We present a reconstruction method involving maximum-likelihood expectation maximization (MLEM) to model Poisson noise as applied to fluorescence molecular tomography (FMT). MLEM is initialized with the output from a sparse reconstruction-based approach, which performs truncated singular value decomposition-based preconditioning followed by fast iterative shrinkage-thresholding algorithm (FISTA) to enforce sparsity. The motivation for this approach is that sparsity information could be accounted for within the initialization, while MLEM would accurately model Poisson noise in the FMT system. Simulation experiments show the proposed method significantly improves images qualitatively and quantitatively. The method results in over 20 times faster convergence compared to uniformly initialized MLEM and improves robustness to noise compared to pure sparse reconstruction. We also theoretically justify the ability of the proposed approach to reduce noise in the background region compared to pure sparse reconstruction. Overall, these results provide strong evidence to model Poisson noise in FMT reconstruction and for application of the proposed reconstruction framework to FMT imaging.

Synchronization-based clustering algorithm for reconstruction of multiple reconstructed targets in fluorescence molecular tomography

Fluorescence molecular tomography (FMT) is an important in vivo molecular imaging technique and has been widely studied in preclinical research. Many methods perform well in the reconstruction of a single fluorescent target but may fail in reconstructing multiple targets because of the severe ill-posedness of the FMT inverse problem. In this paper the original synchronization-inspired clustering algorithm (OSC) is introduced into FMT for resolving multiple targets from the reconstruction result. Based on OSC, a synchronization-based clustering algorithm for FMT (SC-FMT) is developed to further improve location accuracy. Both algorithms utilize the minimum spanning tree to automatically identify the number of the reconstructed targets without prior information and human intervention. A serial of numerical simulation results demonstrates that SC-FMT and OSC can resolve multiple targets robustly and automatically, which also shows the potential of the proposed postprocessing algorithms in FMT reconstruction.

Modulus design multiwavelength polarization microscope for transmission Mueller matrix imaging

We have developed a polarization microscope based on a commercial transmission microscope. We replace the halogen light source by a collimated LED light source module of six different colors. We use achromatic polarized optical elements that can cover the six different wavelength ranges in the polarization state generator (PSG) and polarization state analyzer (PSA) modules. The dual-rotating wave plate method is used to measure the Mueller matrix of samples, which requires the simultaneous rotation of the two quarter-wave plates in both PSG and PSA at certain angular steps. A scientific CCD detector is used as the image receiving module. A LabView-based software is developed to control the rotation angels of the wave plates and the exposure time of the detector to allow the system to run fully automatically in preprogrammed schedules. Standard samples, such as air, polarizers, and quarter-wave plates, are used to calibrate the intrinsic Mueller matrix of optical components, such as the objectives, using the eigenvalue calibration method. Errors due to the images walk-off in the PSA are studied. Errors in the Mueller matrices are below 0.01 using air and polarizer as standard samples. Data analysis based on Mueller matrix transformation and Mueller matrix polarization decomposition is used to demonstrate the potential application of this microscope in pathological diagnosis.

Generalized Adaptive Gaussian Markov Random Field for X-Ray Luminescence Computed Tomography

OBJECTIVE

X-ray luminescence computed tomography (XLCT) is an emerging and promising modality, but suffers from inferior reconstructions and smoothed target shapes. This work aims to improve the image quality with new mathematical framework.

METHODS

We present a Bayesian local regularization framework to tackle the ill-conditioness of XLCT. Different from traditional overall regularization strategies, the proposed method utilizes correlations of neighboring voxels to regularize the solution locally based on generalized adaptive Gaussian Markov random field (GAGMRF), and provides an adjustable parameter to facilitate the edge-preserving property.

RESULTS

Numerical simulations and phantom experiments show that the GAGMRF method yields both high image quality and accurate target shapes.

CONCLUSION

Compared to conventional L2 and L1 regularizations, GAGMRF provides a new and efficient model for high quality imaging based on the Bayesian framework.

SIGNIFICANCE

The GAGMRF method offers a flexible regularization framework to adapt to a wide range of biomedical applications.

Anatomical image-guided fluorescence molecular tomography reconstruction using kernel method

Fluorescence molecular tomography (FMT) is an important in vivo imaging modality to visualize physiological and pathological processes in small animals. However, FMT reconstruction is ill-posed and ill-conditioned due to strong optical scattering in deep tissues, which results in poor spatial resolution. It is well known that FMT image quality can be improved substantially by applying the structural guidance in the FMT reconstruction. An approach to introducing anatomical information into the FMT reconstruction is presented using the kernel method. In contrast to conventional methods that incorporate anatomical information with a Laplacian-type regularization matrix, the proposed method introduces the anatomical guidance into the projection model of FMT. The primary advantage of the proposed method is that it does not require segmentation of targets in the anatomical images. Numerical simulations and phantom experiments have been performed to demonstrate the proposed approach’s feasibility. Numerical simulation results indicate that the proposed kernel method can separate two FMT targets with an edge-to-edge distance of 1 mm and is robust to false-positive guidance and inhomogeneity in the anatomical image. For the phantom experiments with two FMT targets, the kernel method has reconstructed both targets successfully, which further validates the proposed kernel method.

Laplacian manifold regularization method for fluorescence molecular tomography

Sparse regularization methods have been widely used in fluorescence molecular tomography (FMT) for stable three-dimensional reconstruction. Generally, ? 1 -regularization-based methods allow for utilizing the sparsity nature of the target distribution. However, in addition to sparsity, the spatial structure information should be exploited as well. A joint ? 1 and Laplacian manifold regularization model is proposed to improve the reconstruction performance, and two algorithms (with and without Barzilai–Borwein strategy) are presented to solve the regularization model. Numerical studies and in vivo experiment demonstrate that the proposed Gradient projection-resolved Laplacian manifold regularization method for the joint model performed better than the comparative algorithm for ? 1 minimization method in both spatial aggregation and location accuracy.

Cone Beam X-ray Luminescence Computed Tomography Based on Bayesian Method

X-ray luminescence computed tomography (XLCT), which aims to achieve molecular and functional imaging by X-rays, has recently been proposed as a new imaging modality. Combining the principles of X-ray excitation of luminescence-based probes and optical signal detection, XLCT naturally fuses functional and anatomical images and provides complementary information for a wide range of applications in biomedical research. In order to improve the data acquisition efficiency of previously developed narrow-beam XLCT, a cone beam XLCT (CB-XLCT) mode is adopted here to take advantage of the useful geometric features of cone beam excitation. Practically, a major hurdle in using cone beam X-ray for XLCT is that the inverse problem here is seriously ill-conditioned, hindering us to achieve good image quality. In this paper, we propose a novel Bayesian method to tackle the bottleneck in CB-XLCT reconstruction. The method utilizes a local regularization strategy based on Gaussian Markov random field to mitigate the ill-conditioness of CB-XLCT. An alternating optimization scheme is then used to automatically calculate all the unknown hyperparameters while an iterative coordinate descent algorithm is adopted to reconstruct the image with a voxel-based closed-form solution. Results of numerical simulations and mouse experiments show that the self-adaptive Bayesian method significantly improves the CB-XLCT image quality as compared with conventional methods.

Accelerated fast iterative shrinkage thresholding algorithms for sparsity-regularized cone-beam CT image reconstruction

PURPOSE

The development of iterative image reconstruction algorithms for cone-beam computed tomography (CBCT) remains an active and important research area. Even with hardware acceleration, the overwhelming majority of the available 3D iterative algorithms that implement nonsmooth regularizers remain computationally burdensome and have not been translated for routine use in time-sensitive applications such as image-guided radiation therapy (IGRT). In this work, two variants of the fast iterative shrinkage thresholding algorithm (FISTA) are proposed and investigated for accelerated iterative image reconstruction in CBCT.

METHODS

Algorithm acceleration was achieved by replacing the original gradient-descent step in the FISTAs by a subproblem that is solved by use of the ordered subset simultaneous algebraic reconstruction technique (OS-SART). Due to the preconditioning matrix adopted in the OS-SART method, two new weighted proximal problems were introduced and corresponding fast gradient projection-type algorithms were developed for solving them. We also provided efficient numerical implementations of the proposed algorithms that exploit the massive data parallelism of multiple graphics processing units.

RESULTS

The improved rates of convergence of the proposed algorithms were quantified in computer-simulation studies and by use of clinical projection data corresponding to an IGRT study. The accelerated FISTAs were shown to possess dramatically improved convergence properties as compared to the standard FISTAs. For example, the number of iterations to achieve a specified reconstruction error could be reduced by an order of magnitude. Volumetric images reconstructed from clinical data were produced in under 4 min.

CONCLUSIONS

The FISTA achieves a quadratic convergence rate and can therefore potentially reduce the number of iterations required to produce an image of a specified image quality as compared to first-order methods. We have proposed and investigated accelerated FISTAs for use with two nonsmooth penalty functions that will lead to further reductions in image reconstruction times while preserving image quality. Moreover, with the help of a mixed sparsity-regularization, better preservation of soft-tissue structures can be potentially obtained. The algorithms were systematically evaluated by use of computer-simulated and clinical data sets.

Structure-adaptive CBCT reconstruction using weighted total variation and Hessian penalties

The exposure of normal tissues to high radiation during cone-beam CT (CBCT) imaging increases the risk of cancer and genetic defects. Statistical iterative algorithms with the total variation (TV) penalty have been widely used for low dose CBCT reconstruction, with state-of-the-art performance in suppressing noise and preserving edges. However, TV is a first-order penalty and sometimes leads to the so-called staircase effect, particularly over regions with smooth intensity transition in the reconstruction images. A second-order penalty known as the Hessian penalty was recently used to replace TV to suppress the staircase effect in CBCT reconstruction at the cost of slightly blurring object edges. In this study, we proposed a new penalty, the TV-H, which combines TV and Hessian penalties for CBCT reconstruction in a structure-adaptive way. The TV-H penalty automatically differentiates the edges, gradual transition and uniform local regions within an image using the voxel gradient, and adaptively weights TV and Hessian according to the local image structures in the reconstruction process. Our proposed penalty retains the benefits of TV, including noise suppression and edge preservation. It also maintains the structures in regions with gradual intensity transition more successfully. A majorization-minimization (MM) approach was designed to optimize the objective energy function constructed with the TV-H penalty. The MM approach employed a quadratic upper bound of the original objective function, and the original optimization problem was changed to a series of quadratic optimization problems, which could be efficiently solved using the Gauss-Seidel update strategy. We tested the reconstruction algorithm on two simulated digital phantoms and two physical phantoms. Our experiments indicated that the TV-H penalty visually and quantitatively outperformed both TV and Hessian penalties.

Fast direct reconstruction strategy of dynamic fluorescence molecular tomography using graphics processing units

Dynamic fluorescence molecular tomography (DFMT) is a valuable method to evaluate the metabolic process of contrast agents in different organs in vivo, and direct reconstruction methods can improve the temporal resolution of DFMT. However, challenges still remain due to the large time consumption of the direct reconstruction methods. An acceleration strategy using graphics processing units (GPU) is presented. The procedure of conjugate gradient optimization in the direct reconstruction method is programmed using the compute unified device architecture and then accelerated on GPU. Numerical simulations and in vivo experiments are performed to validate the feasibility of the strategy. The results demonstrate that, compared with the traditional method, the proposed strategy can reduce the time consumption by ∼90% without a degradation of quality.

Reconstruction of difference in sequential CT studies using penalized likelihood estimation

Characterization of anatomical change and other differences is important in sequential computed tomography (CT) imaging, where a high-fidelity patient-specific prior image is typically present, but is not used, in the reconstruction of subsequent anatomical states. Here, we introduce a penalized likelihood (PL) method called reconstruction of difference (RoD) to directly reconstruct a difference image volume using both the current projection data and the (unregistered) prior image integrated into the forward model for the measurement data. The algorithm utilizes an alternating minimization to find both the registration and reconstruction estimates. This formulation allows direct control over the image properties of the difference image, permitting regularization strategies that inhibit noise and structural differences due to inconsistencies between the prior image and the current data. Additionally, if the change is known to be local, RoD allows local acquisition and reconstruction, as opposed to traditional model-based approaches that require a full support field of view (or other modifications). We compared the performance of RoD to a standard PL algorithm, in simulation studies and using test-bench cone-beam CT data. The performances of local and global RoD approaches were similar, with local RoD providing a significant computational speedup. In comparison across a range of data with differing fidelity, the local RoD approach consistently showed lower error (with respect to a truth image) than PL in both noisy data and sparsely sampled projection scenarios. In a study of the prior image registration performance of RoD, a clinically reasonable capture ranges were demonstrated. Lastly, the registration algorithm had a broad capture range and the error for reconstruction of CT data was 35% and 20% less than filtered back-projection for RoD and PL, respectively. The RoD has potential for delivering high-quality difference images in a range of sequential clinical scenarios including image-guided surgeries and treatments where accurate and quantitative assessments of anatomical change is desired.

Patch-based anisotropic diffusion scheme for fluorescence diffuse optical tomography--part 2: image reconstruction

Fluorescence diffuse optical tomography (fDOT) provides 3D images of fluorescence distributions in biological tissue, which represent molecular and cellular processes. The image reconstruction problem is highly ill-posed and requires regularisation techniques to stabilise and find meaningful solutions. Quadratic regularisation tends to either oversmooth or generate very noisy reconstructions, depending on the regularisation strength. Edge preserving methods, such as anisotropic diffusion regularisation (AD), can preserve important features in the fluorescence image and smooth out noise. However, AD has limited ability to distinguish an edge from noise. We propose a patch-based anisotropic diffusion regularisation (PAD), where regularisation strength is determined by a weighted average according to the similarity between patches around voxels within a search window, instead of a simple local neighbourhood strategy. However, this method has higher computational complexity and, hence, we wavelet compress the patches (PAD-WT) to speed it up, while simultaneously taking advantage of the denoising properties of wavelet thresholding. Furthermore, structural information can be incorporated into the image reconstruction with PAD-WT to improve image quality and resolution. In this case, the weights used to average voxels in the image are calculated using the structural image, instead of the fluorescence image. The regularisation strength depends on both structural and fluorescence images, which guarantees that the method can preserve fluorescence information even when it is not structurally visible in the anatomical images. In part 1, we tested the method using a denoising problem. Here, we use simulated and in vivo mouse fDOT data to assess the algorithm performance. Our results show that the proposed PAD-WT method provides high quality and noise free images, superior to those obtained using AD.

Reverse-Time Migration Based Optical Imaging

We theoretically demonstrated a new optical imaging technique based on reverse-time migration (RTM) for reconstructing optical structures in homogeneous media for the first time. RTM is a powerful wave-equation-based method to reconstruct the image of the structure by modeling the wave propagation inside the media with both forward modeling and reverse-time extrapolation. While RTM is commonly used with acoustic seismic waves, this paper represents the first effort to develop optical RTM imaging method for biomedical research. To refine the image quality, we further developed new methods to suppress the low-wavenumber artifact (LWA). When compared with the conventional means for LWA suppression such as Laplacian filtering, illumination normalization, and the ratio method, our new derivative-based and power-image methods are able to significantly reduce LWA, resulting in high-quality reconstructed images with sufficient contrasts and spatial resolutions for structure identification. The optical RTM imaging technique may provide a new platform for non-invasive optical imaging of structures in deep layers of tissues for biomedical applications.

A Sparsity-Constrained Preconditioned Kaczmarz Reconstruction Method for Fluorescence Molecular Tomography

Fluorescence molecular tomography (FMT) is an imaging technique that can localize and quantify fluorescent markers to resolve biological processes at molecular and cellular levels. Owing to a limited number of measurements and a large number of unknowns as well as the diffusive transport of photons in biological tissues, the inverse problem in FMT is usually highly ill-posed. In this work, a sparsity-constrained preconditioned Kaczmarz (SCP-Kaczmarz) method is proposed to reconstruct the fluorescent target for FMT. The SCP-Kaczmarz method uses the preconditioning strategy to minimize the correlation between the rows of the forward matrix and constrains the Kaczmarz iteration results to be sparse. Numerical simulation and phantom and in vivo experiments were performed to test the efficiency of the proposed method. The results demonstrate that both the convergence and accuracy of the proposed method are improved compared with the classical memory-efficient low-cost Kaczmarz method.

3D mouse shape reconstruction based on phase-shifting algorithm for fluorescence molecular tomography imaging system

This work introduces a fast, low-cost, robust method based on fringe pattern and phase shifting to obtain three-dimensional (3D) mouse surface geometry for fluorescence molecular tomography (FMT) imaging. We used two pico projector/webcam pairs to project and capture fringe patterns from different views. We first calibrated the pico projectors and the webcams to obtain their system parameters. Each pico projector/webcam pair had its own coordinate system. We used a cylindrical calibration bar to calculate the transformation matrix between these two coordinate systems. After that, the pico projectors projected nine fringe patterns with a phase-shifting step of 2π/9 onto the surface of a mouse-shaped phantom. The deformed fringe patterns were captured by the corresponding webcam respectively, and then were used to construct two phase maps, which were further converted to two 3D surfaces composed of scattered points. The two 3D point clouds were further merged into one with the transformation matrix. The surface extraction process took less than 30 seconds. Finally, we applied the Digiwarp method to warp a standard Digimouse into the measured surface. The proposed method can reconstruct the surface of a mouse-sized object with an accuracy of 0.5 mm, which we believe is sufficient to obtain a finite element mesh for FMT imaging. We performed an FMT experiment using a mouse-shaped phantom with one embedded fluorescence capillary target. With the warped finite element mesh, we successfully reconstructed the target, which validated our surface extraction approach.

Reconstruction for 3D PET Based on Total Variation Constrained Direct Fourier Method

This paper presents a total variation (TV) regularized reconstruction algorithm for 3D positron emission tomography (PET). The proposed method first employs the Fourier rebinning algorithm (FORE), rebinning the 3D data into a stack of ordinary 2D data sets as sinogram data. Then, the resulted 2D sinogram are ready to be reconstructed by conventional 2D reconstruction algorithms. Given the locally piece-wise constant nature of PET images, we introduce the total variation (TV) based reconstruction schemes. More specifically, we formulate the 2D PET reconstruction problem as an optimization problem, whose objective function consists of TV norm of the reconstructed image and the data fidelity term measuring the consistency between the reconstructed image and sinogram. To solve the resulting minimization problem, we apply an efficient methods called the Bregman operator splitting algorithm with variable step size (BOSVS). Experiments based on Monte Carlo simulated data and real data are conducted as validations. The experiment results show that the proposed method produces higher accuracy than conventional direct Fourier (DF) (bias in BOSVS is 70% of ones in DF, variance of BOSVS is 80% of ones in DF).

Experimental Comparison of Continuous-Wave and Frequency-Domain Fluorescence Tomography in a Commercial Multi-Modal Scanner

The performance evaluation of a variety of small animal tomography measurement approaches and algorithms for recovery of fluorescent absorption cross section has not been conducted. Herein, we employed an intensified CCD system installed in a commercial small animal CT (Computed Tomography) scanner to compare image reconstructions from time-independent, continuous wave (CW) measurements and from time-dependent, frequency domain (FD) measurements in a series of physical phantoms specifically designed for evaluation. Comparisons were performed as a function of (1) number of projections, (2) the level of preprocessing filters used to improve the signal-to-noise ratio (SNR), (3) endogenous heterogeneity of optical properties, as well as in the cases of (4) two fluorescent targets and (5) a mouse-shaped phantom. Assessment of quantitative recovery of fluorescence absorption cross section was performed using a fully parallel, regularization-free, linear reconstruction algorithm with diffusion approximation (DA) and high order simplified spherical harmonics ( SPN) approximation to the radiative transport equation (RTE). The results show that while FD measurements may result in superior image reconstructions over CW measurements, data acquisition times are significantly longer, necessitating further development of multiple detector/source configurations, improved data read-out rates, and detector technology. FD measurements with SP3 reconstructions enabled better quantitative recovery of fluorescent target strength, but required increased computational expense. Despite the developed parallel reconstruction framework being able to achieve more than 60 times speed increase over sequential implementation, further development in faster parallel acceleration strategies for near-real time and real-time image recovery and more precise forward solution is necessary.

Fluorescence molecular tomography in the second near-infrared window

Fluorescence molecular tomography (FMT), an in vivo noninvasive imaging technology, can provide localization and quantification information for deep fluorophores. Light at wavelengths in the near-infrared (NIR-I) window from 650 nm to 950 nm has conventionally been chosen for FMT. In this study, we introduced longer NIR wavelengths within the 1100 nm to 1400 nm range, known as the "second NIR spectral window" (NIR-II). A singular-value analysis method was used to demonstrate the utility and advantages of using the NIR-II for FMT, and experiments showed an improvement in the spatial resolution in phantom studies.

Improved sparse reconstruction for fluorescence molecular tomography with L1/2 regularization

Fluorescence molecular tomography (FMT) is a promising imaging technique that allows in vivo visualization of molecular-level events associated with disease progression and treatment response. Accurate and efficient 3D reconstruction algorithms will facilitate the wide-use of FMT in preclinical research. Here, we utilize L1/2-norm regularization for improving FMT reconstruction. To efficiently solve the nonconvex L1/2-norm penalized problem, we transform it into a weighted L1-norm minimization problem and employ a homotopy-based iterative reweighting algorithm to recover small fluorescent targets. Both simulations on heterogeneous mouse model and in vivo experiments demonstrated that the proposed L1/2-norm method outperformed the comparative L1-norm reconstruction methods in terms of location accuracy, spatial resolution and quantitation of fluorescent yield. Furthermore, simulation analysis showed the robustness of the proposed method, under different levels of measurement noise and number of excitation sources.

Construction of mouse phantoms from segmented CT scan data for radiation dosimetry studies

We present the complete construction methodology for an anatomically accurate mouse phantom made using materials which mimic the characteristics of tissue, lung, and bone for radiation dosimetry studies. Phantoms were constructed using 2 mm thick slices of tissue equivalent material which was precision machined to clear regions for insertion of lung and bone equivalent material where appropriate. Images obtained using a 3D computed tomography (CT) scan clearly indicate regions of tissue, lung, and bone that match their position within the original mouse CT scan. Additionally, radiographic films are used with the phantom to demonstrate dose mapping capabilities. The construction methodology presented here can be quickly and easily adapted to create a phantom of any specific small animal given a segmented CT scan of the animal. These physical phantoms are a useful tool to examine individual organ dose and dosimetry within mouse systems that are complicated by density inhomogeneity due to bone and lung regions.

A Novel Region Reconstruction Method for Fluorescence Molecular Tomography

Fluorescence molecular tomography (FMT) could exploit the distribution of fluorescent biomarkers that target tumors accurately and effectively, which enables noninvasive real-time 3-D visualization as well as quantitative analysis of small tumors in small animal studies in vivo. Due to the difficulties of reconstruction, continuous efforts are being made to find more practical and efficient approaches to accurately obtain the characteristics of fluorescent regions inside biological tissues. In this paper, we propose a region reconstruction method for FMT, which is defined as an L1-norm regularization piecewise constant level set approach. The proposed approach adopts a priori information including the sparsity of the fluorescent sources and the fluorescent contrast between the target and background. When the contrast of different fluorescent sources is low to a certain degree, our approach can simultaneously solve the detection and characterization problems for the reconstruction of FMT. To evaluate the performance of the region reconstruction method, numerical phantom experiments and in vivo bead-implanted mouse experiments were performed. The results suggested that the proposed region reconstruction method was able to reconstruct the features of the fluorescent regions accurately and effectively, and the proposed method was able to be feasibly adopted in in vivo application.

Localizing fluorophore (centroid) inside a scattering medium by depth perturbation

Fluorescence molecular tomography (FMT) imaging can be used to determine the location, size, and biodistribution of fluorophore biomarkers inside tissues. Yet when using FMT in the reflectance geometry it is challenging to accurately localize fluorophores. A depth perturbation method is proposed to determine the centroid of fluorophore inside a tissue-like medium. Through superposition of a known thin optical phantom onto the medium surface, the fluorophore depth is deliberately perturbed and signal localization is improved in a stable way. We hypothesize that the fluorophore centroid can be better localized through use of this fluorescent intensity variation resulting from the depth perturbation. This hypothesis was tested in tissue-like phantoms. The results show that a small-size fluorophore inclusion (1.2 mm(3)volume, depth up to 4.8 mm) can be localized by the method with an error of 0.2 to 0.3 mm. The method is also proven to be capable of handling multiple fluorescent inclusion conditions with the assistance of other strategies. Additionally, our further studies showed that the method's performance in the presence of background fluorophores indicated that the small inclusion could be located at a 1.8 (3.8) mm depth with accurate localization only when its concentration was not <10 (100) times the background level.