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

TSPE: Reconstruction of multi-morphological tumors of NIR-II fluorescence molecular tomography based on positional encoding

BACKGROUND AND OBJECTIVE

Fluorescence molecular tomography (FMT) is a noninvasive and highly sensitive imaging modality, which can display 3D visualization of tumors by reconstructing fluorescence probes' distribution. However, existing methods mostly ignore positional information, which includes spatial structure information crucial for the reconstruction of light sources. This limits the reconstruction accuracy of light sources with multiple morphologies. Therefore, to our best knowledge, we for the first time integrated positional encoding into the FMT task, enabling the incorporation of high-frequency spatial structure information.

METHODS

We proposed a three-stage network embedded with a positional encoding module (TSPE) to perform high reconstruction accuracy of tumors with multiple morphologies. Additionally, our study focused on NIR-II which had less severe scattering problems and higher imaging accuracy than NIR-I.

RESULTS

The simulation experiments demonstrated that TSPE achieved high reconstruction accuracy in NIR-II FMT, with the barycenter error (BCE) for single-tumor reconstruction reaching 0.18 mm, representing a 14 % reduction compared to other methods. TSPE more accurately distinguished adjacent multi-morphological tumors with a minimal edge-to-edge distance (EED) of 0.3 mm. In vivo experiments also showed that TSPE could achieve more accurate reconstruction of tumors compared with other methods.

CONCLUSIONS

The proposed method can achieve the best reconstruction performance. It has potential to promote the development of NIR-II FMT and its preclinical application.

Monotone Accelerated Proximal Gradient Network For Bioluminescence Tomography Reconstruction

Bioluminescence tomography (BLT) is a noninvasive technique designed to enable three-dimensional (3D) visualization and quantification of viable tumor cells in living organisms. However, despite the excellent sensitivity and specificity of bioluminescence imaging (BLI), BLT is limited by the photon scattering effect and ill-posed inverse problem. To overcome this problem, regularization algorithms have been widely studied and achieved impressive results. Recently, reconstruction approaches based on deep learning have shown great potential in optical tomography modalities. However, the parameter selection of the regularization algorithm and the poor interpretability of deep learning methods have become the key factors to affect the reconstruction results and hinder its applicability. In addition, the spatial relationship between adjacent elements in the BLT data is a classical non-Euclidean data. Therefore, to mitigate the effects of this problem, in this paper, we proposed a novel Monotone accelerated proximal gradient network (MAPG-net) for bioluminescence tomography reconstruction by combining the advantages of the regularization method and Graph attention (GAT). The MAPG-net naturally inherits the solution constraints from the regularization-based methods framework, thus enhancing the stability and interpretability of the network. The numerical experiments confirmed that the proposed network has excellent performance.

Highly robust reconstruction framework for three-dimensional optical imaging based on physical model constrained neural networks

Objective. The reconstruction of three-dimensional optical imaging that can quantitatively acquire the target distribution from surface measurements is a serious ill-posed problem. Traditional regularization-based reconstruction can solve such ill-posed problem to a certain extent, but its accuracy is highly dependent ona priorinformation, resulting in a less stable and adaptable method. Data-driven deep learning-based reconstruction avoids the errors of light propagation models and the reliance on experience and a prior by learning the mapping relationship between the surface light distribution and the target directly from the dataset. However, the acquisition of the training dataset and the training of the network itself are time consuming, and the high dependence of the network performance on the training dataset results in a low generalization ability. The objective of this work is to develop a highly robust reconstruction framework to solve the existing problems.Approach. This paper proposes a physical model constrained neural networks-based reconstruction framework. In the framework, the neural networks are to generate a target distribution from surface measurements, while the physical model is used to calculate the surface light distribution based on this target distribution. The mean square error between the calculated surface light distribution and the surface measurements is then used as a loss function to optimize the neural network. To further reduce the dependence ona prioriinformation, a movable region is randomly selected and then traverses the entire solution interval. We reconstruct the target distribution in this movable region and the results are used as the basis for its next movement.Main Results. The performance of the proposed framework is evaluated with a series of simulations andin vivoexperiment, including accuracy robustness of different target distributions, noise immunity, depth robustness, and spatial resolution. The results collectively demonstrate that the framework can reconstruct targets with a high accuracy, stability and versatility.Significance. The proposed framework has high accuracy and robustness, as well as good generalizability. Compared with traditional regularization-based reconstruction methods, it eliminates the need to manually delineate feasible regions and adjust regularization parameters. Compared with emerging deep learning assisted methods, it does not require any training dataset, thus saving a lot of time and resources and solving the problem of poor generalization and robustness of deep learning methods. Thus, the framework opens up a new perspective for the reconstruction of three-dimension optical imaging.

Automated Restarting Fast Proximal Gradient Descent Method for Single-View Cone-Beam X-ray Luminescence Computed Tomography Based on Depth Compensation

Single-view cone-beam X-ray luminescence computed tomography (CB-XLCT) has recently gained attention as a highly promising imaging technique that allows for the efficient and rapid three-dimensional visualization of nanophosphor (NP) distributions in small animals. However, the reconstruction performance is hindered by the ill-posed nature of the inverse problem and the effects of depth variation as only a single view is acquired. To tackle this issue, we present a methodology that integrates an automated restarting strategy with depth compensation to achieve reconstruction. The present study employs a fast proximal gradient descent (FPGD) method, incorporating L0 norm regularization, to achieve efficient reconstruction with accelerated convergence. The proposed approach offers the benefit of retrieving neighboring multitarget distributions without the need for CT priors. Additionally, the automated restarting strategy ensures reliable reconstructions without the need for manual intervention. Numerical simulations and physical phantom experiments were conducted using a custom CB-XLCT system to demonstrate the accuracy of the proposed method in resolving adjacent NPs. The results showed that this method had the lowest relative error compared to other few-view techniques. This study signifies a significant progression in the development of practical single-view CB-XLCT for high-resolution 3-D biomedical imaging.

Regularized reconstruction based on joint smoothly clipped absolute deviation regularization and graph manifold learning for fluorescence molecular tomography

Objective.Fluorescence molecular tomography (FMT) is an optical imaging modality that provides high sensitivity and low cost, which can offer the three-dimensional distribution of biomarkers by detecting the fluorescently labeled probe noninvasively. In the field of preclinical cancer diagnosis and treatment, FMT has gained significant traction. Nonetheless, the current FMT reconstruction results suffer from unsatisfactory morphology and location accuracy of the fluorescence distribution, primarily due to the light scattering effect and the ill-posed nature of the inverse problem.Approach.To address these challenges, a regularized reconstruction method based on joint smoothly clipped absolute deviation regularization and graph manifold learning (SCAD-GML) for FMT is presented in this paper. The SCAD-GML approach combines the sparsity of the fluorescent sources with the latent manifold structure of fluorescent source distribution to achieve more accurate and sparse reconstruction results. To obtain the reconstruction results efficiently, the non-convex gradient descent iterative method is employed to solve the established objective function. To assess the performance of the proposed SCAD-GML method, a comprehensive evaluation is conducted through numerical simulation experiments as well asin vivoexperiments.Main results.The results demonstrate that the SCAD-GML method outperforms other methods in terms of both location and shape recovery of fluorescence biomarkers distribution.Siginificance.These findings indicate that the SCAD-GML method has the potential to advance the application of FMT inin vivobiological research.

3D-deep optical learning: a multimodal and multitask reconstruction framework for optical molecular tomography

Optical molecular tomography (OMT) is an emerging imaging technique. To date, the poor universality of reconstruction algorithms based on deep learning for various imaged objects and optical probes limits the development and application of OMT. In this study, based on a new mapping representation, a multimodal and multitask reconstruction framework-3D deep optical learning (3DOL), was presented to overcome the limitations of OMT in universality by decomposing it into two tasks, optical field recovery and luminous source reconstruction. Specifically, slices of the original anatomy (provided by computed tomography) and boundary optical measurement of imaged objects serve as inputs of a recurrent convolutional neural network encoded parallel to extract multimodal features, and 2D information from a few axial planes within the samples is explicitly incorporated, which enables 3DOL to recognize different imaged objects. Subsequently, the optical field is recovered under the constraint of the object geometry, and then the luminous source is segmented by a learnable Laplace operator from the recovered optical field, which obtains stable and high-quality reconstruction results with extremely few parameters. This strategy enable 3DOL to better understand the relationship between the boundary optical measurement, optical field, and luminous source to improve 3DOL's ability to work in a wide range of spectra. The results of numerical simulations, physical phantoms, and in vivo experiments demonstrate that 3DOL is a compatible deep-learning approach to tomographic imaging diverse objects. Moreover, the fully trained 3DOL under specific wavelengths can be generalized to other spectra in the 620-900 nm NIR-I window.

Structure-fused deep 3D hierarchical network: A bioluminescence tomography scheme for different imaging objects

Monte Carlo eXtreme (MCX) method has a unique advantage for deep neural network based bioluminescence tomography (BLT) reconstruction. However, this method ignores the distribution of sources energy and relies on the determined tissue structure. In this paper, a deep 3D hierarchical reconstruction network for BLT was proposed where the inputs were divided into two parts -- bioluminescence image (BLI) and anatomy of the imaged object by CT. Firstly, a parallel encoder is used to feature the original BLI & CT slices and integrate their features to distinguish the different tissue structure of imaging objects; Secondly, GRU is used to fit the spatial information of different slices and convert it into 3D features; Finally, the 3D features are decoded to the spacial and energy information of source by a symmetrical decoding structure. Our research suggested that this method can effectively compute the radiation intensity and the spatial distribution of the source for different imaging object.

K-CapsNet: K-Nearest Neighbor Based Convolution Capsule Network for Cerenkov Luminescence Tomography Reconstruction

Cerenkov luminescence tomography (CLT) has received significant attention as a promising imaging modality that can display the three-dimensional (3D) distribution of radioactive probes. However, the reconstruction of CLT suffers from severe ill-posed problem. It is difficult for traditional model-based method to obtain satisfactory result. Recently, deep learning-based method have shown great potential for accurate and efficient CLT reconstruction. In this study, a KNN-based convolution capsule network, named K-CapsNet, is proposed for cerenkov luminescence tomography. In K-CapsNet, the surface photon intensity is encoded in capsule form. The KNN-based convolution and K-means clustering are proposed for efficient encoding. Numerical simulation experiments have been carried out to verify the performance of K-CapsNet, and the results show that it performs superior in source localization and morphological restoration compared with existing methods.

FISTA-NET: Deep Algorithm Unrolling for Cerenkov luminescence tomography

Cerenkov luminescence tomography (CLT) is a highly sensitive and promising imaging technique that can be used to reconstruct the three-dimensional distribution of radioactive probes in living animals. However, the accuracy of CLT reconstruction is limited by the simplified radiative transfer equation and ill-conditioned inverse problem. To address this issue, we propose a model-based deep learning network that combines the neural network with a model-based approach to enhance the performance of CLT reconstruction. The Fast Iterative Shrinkage Thresholding Algorithm (FISTA), a traditional model-based approach, is expanded into a deep network (known as FISTA-NET). Each layer in the network represents an iteration of the algorithm steps, and connecting these layers can form a deep neural network. In addition, different from the traditional FISTA, the key parameters in FISTA, such as gradient step size and threshold value, can be learned through training data without manual production. To evaluate the performance of FISTA-NET, numerical simulation experiments were conducted, which demonstrate its excellent positioning and shape recovery abilities.Clinical Relevance-This indicates that FISTA-NET strategy can significantly improve the quality of CLT reconstruction, which is further beneficial to the assessment of disease activity and treatment effect based on CLT.

Deep background-mismodeling-learned reconstruction for high-accuracy fluorescence diffuse optical tomography

We present a deep background-mismodeling-learned reconstruction framework for high-accuracy fluorescence diffuse optical tomography (FDOT). A learnable regularizer incorporating background mismodeling is formulated in the form of certain mathematical constraints. The regularizer is then learned to obtain the background mismodeling automatically using a physics-informed deep network implicitly. Here, a deep-unrolled FIST-Net for optimizing L1-FDOT is specially designed to obtain fewer learning parameters. Experiments show that the accuracy of FDOT is significantly improved via implicitly learning the background mismodeling, which proves the validity of the deep background-mismodeling-learned reconstruction. The proposed framework can also be used as a general method to improve a class of image modalities based on linear inverse problems with unknown background modeling errors.

Two-stage deep learning method for sparse-view fluorescence molecular tomography reconstruction

Fluorescence molecular tomography (FMT) is a preclinical optical tomographic imaging technique that can trace various physiological and pathological processes at the cellular or even molecular level. Reducing the number of FMT projection views can improve the data acquisition speed, which is significant in applications such as dynamic problems. However, a reduction in the number of projection views will dramatically aggravate the ill-posedness of the FMT inverse problem and lead to significant degradation of the reconstructed images. To deal with this problem, we have proposed a deep-learning-based reconstruction method for sparse-view FMT that only uses four perpendicular projection views and divides the image reconstruction into two stages: image restoration and inverse Radon transform. In the first stage, the projection views of the surface fluorescence are restored to eliminate the blur derived from photon diffusion through a fully convolutional neural network. In the second stage, another convolutional neural network is used to implement the inverse Radon transform between the restored projections from the first stage and the reconstructed transverse slices. Numerical simulation and phantom and mouse experiments are carried out. The results show that the proposed method can effectively deal with the image reconstruction problem of sparse-view FMT.

Efficient FMT reconstruction based on L1-αL2 regularization via half-quadratic splitting and a two-probe separation light source strategy

Fluorescence molecular tomography (FMT) can achieve noninvasive, high-contrast, high-sensitivity three-dimensional imaging in vivo by relying on a variety of fluorescent molecular probes, and has excellent clinical transformation prospects in the detection of tumors in vivo. However, the limited surface fluorescence makes the FMT reconstruction have some ill-posedness, and it is difficult to obtain the ideal reconstruction effect. In this paper, two different emission fluorescent probes and L 1-L 2 regularization are combined to improve the temporal and spatial resolution of FMT visual reconstruction by introducing the weighting factor α and a half-quadratic splitting alternating optimization (HQSAO) iterative algorithm. By introducing an auxiliary variable, the HQSAO method breaks the sparse FMT reconstruction task into two subproblems that can be solved in turn: simple reconstruction and image denoising. The weight factor α (α>1) can increase the weight of nonconvex terms to further promote the sparsity of the algorithm. Importantly, this paper combines two different dominant fluorescent probes to achieve high-quality reconstruction of dual light sources. The performance of the proposed reconstruction strategy was evaluated by digital mouse and nude mouse single/dual light source models. The simulation results show that the HQSAO iterative algorithm can achieve more excellent positioning accuracy and morphology distribution in a shorter time. In vivo experiments also further prove that the HQSAO algorithm has advantages in light source information preservation and artifact suppression. In particular, the introduction of two main emission fluorescent probes makes it easy to separate and reconstruct the dual light sources. When it comes to localization and three-dimensional morphology, the results of the reconstruction are much better than those using a fluorescent probe, which further facilitates the clinical transformation of FMT.

Robust transformed l1 metric for fluorescence molecular tomography

BACKGROUND AND OBJECTIVE

Fluorescence molecular tomography (FMT) is a non-invasive molecular imaging modality that can be used to observe the three-dimensional distribution of fluorescent probes in vivo. FMT is a promising imaging technique in clinical and preclinical research that has attracted significant attention. Numerous regularization based reconstruction algorithms have been proposed. However, traditional algorithms that use the squared l₂-norm distance usually exaggerate the influence of noise and measurement and calculation errors, and their robustness cannot be guaranteed.

METHODS

In this study, we propose a novel robust transformed l₁ (TL1) metric that interpolates l₀ and l₁ norms through a nonnegative parameter α∈(0,+∞). The TL1 metric looks like the l_p-norm with p∈(0,1). These are markedly different because TL1 metric has two properties, boundedness and Lipschitz-continuity, which make the TL1 criterion suitable distance metric, particularly for robustness, owing to its stronger noise suppression. Subsequently, we apply the proposed metric to FMT and build a robust model to reduce the influence of noise. The nonconvexity of the proposed model made direct optimization difficult, and a continuous optimization method was developed to solve the model. The problem was converted into a difference in convex programming problem for the TL1 metric (DCATL1), and the corresponding algorithm converged linearly.

RESULTS

Various numerical simulations and in vivo bead-implanted mouse experiments were conducted to verify the performance of the proposed method. The experimental results show that the DCATL1 algorithm is more robust than the state-of-the-art approaches and achieves better source localization and morphology recovery.

CONCLUSIONS

The in vivo experiments showed that DCATL1 can be used to visualize the distribution of fluorescent probes inside biological tissues and promote preclinical application in small animals, demonstrating the feasibility and effectiveness of the proposed method.

Generalized conditional gradient method with adaptive regularization parameters for fluorescence molecular tomography

Fluorescence molecular tomography (FMT) is an optical imaging technology with the ability of visualizing the three-dimensional distribution of fluorescently labelled probes in vivo. However, due to the light scattering effect and ill-posed inverse problems, obtaining satisfactory FMT reconstruction is still a challenging problem. In this work, to improve the performance of FMT reconstruction, we proposed a generalized conditional gradient method with adaptive regularization parameters (GCGM-ARP). In order to make a tradeoff between the sparsity and shape preservation of the reconstruction source, and to maintain its robustness, elastic-net (EN) regularization is introduced. EN regularization combines the advantages of L₁-norm and L₂-norm, and overcomes the shortcomings of traditional L_p-norm regularization, such as over-sparsity, over-smoothness, and non-robustness. Thus, the equivalent optimization formulation of the original problem can be obtained. To further improve the performance of the reconstruction, the L-curve is adopted to adaptively adjust the regularization parameters. Then, the generalized conditional gradient method (GCGM) is used to split the minimization problem based on EN regularization into two simpler sub-problems, which are determining the direction of the gradient and the step size. These sub-problems are addressed efficiently to obtain more sparse solutions. To assess the performance of our proposed method, a series of numerical simulation experiments and in vivo experiments were implemented. The experimental results show that, compared with other mathematical reconstruction methods, GCGM-ARP method has the minimum location error (LE) and relative intensity error (RIE), and the maximum dice coefficient (Dice) in the case of different sources number or shape, or Gaussian noise of 5%-25%. This indicates that GCGM-ARP has superior reconstruction performance in source localization, dual-source resolution, morphology recovery, and robustness. In conclusion, the proposed GCGM-ARP is an effective and robust strategy for FMT reconstruction in biomedical application.

An adaptive parameter selection strategy based on maximizing the probability of data for robust fluorescence molecular tomography reconstruction

To alleviate the ill-posed of the inverse problem in fluorescent molecular tomography (FMT), many regularization methods based on L₂ or L₁ norm have been proposed. Whereas, the quality of regularization parameters affects the performance of the reconstruction algorithm. Some classical parameter selection strategies usually need initialization of parameter range and high computing costs, which is not universal in the practical application of FMT. In this paper, an universally applicable adaptive parameter selection method based on maximizing the probability of data (MPD) strategy was proposed. This strategy used maximum a posteriori (MAP) estimation and maximum likelihood (ML) estimation to establish a regularization parameters model. The stable optimal regularization parameters can be determined by multiple iterative estimates. Numerical simulations and in vivo experiments show that MPD strategy can obtain stable regularization parameters for both regularization algorithms based on L₂ or L₁ norm and achieve good reconstruction performance.

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.

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.

Demonstration of Neural Networks to Reconstruct Temperatures from Simulated Fluorescent Data Toward Use in Bio-microfluidics

Biological systems often have a narrow temperature range of operation, which require highly accurate spatially resolved temperature measurements, often near ±0.1 K. However, many temperature sensors cannot meet both accuracy and spatial distribution requirements, often because their accuracy is limited by data fitting and temperature reconstruction models. Machine learning algorithms have the potential to meet this need, but their usage in generating spatial distributions of temperature is severely lacking in the literature. This work presents the first instance of using neural networks to process fluorescent images to map the spatial distribution of temperature. Three standard network architectures were investigated using non-spatially resolved fluorescent thermometry (simply-connected feed-forward network) or during image or pixel identification (U-net and convolutional neural network, CNN). Simulated fluorescent images based on experimental data were generated based on known temperature distributions where Gaussian white noise with a standard deviation of ±0.1 K was added. The poor results from these standard networks motivated the creation of what is termed a moving CNN, with an RMSE error of ±0.23 K, where the elements of the matrix represent the neighboring pixels. Finally, the performance of this MCNN is investigated when trained and applied to three distinctive temperature distributions characteristic within microfluidic devices, where the fluorescent image is simulated at either three or five different wavelengths. The results demonstrate that having a minimum of 10 ^3.5 data points per temperature and the broadest range of temperatures during training provides temperature predictions nearest to the true temperatures of the images, with a minimum RMSE of ±0.15 K. When compared to traditional curve fitting techniques, this work demonstrates that greater accuracy when spatially mapping temperature from fluorescent images can be achieved when using convolutional neural networks.

Self-Training Strategy Based on Finite Element Method for Adaptive Bioluminescence Tomography Reconstruction

Bioluminescence tomography (BLT) is a promising pre-clinical imaging technique for a wide variety of biomedical applications, which can non-invasively reveal functional activities inside living animal bodies through the detection of visible or near-infrared light produced by bioluminescent reactions. Recently, reconstruction approaches based on deep learning have shown great potential in optical tomography modalities. However, these reports only generate data with stationary patterns of constant target number, shape, and size. The neural networks trained by these data sets are difficult to reconstruct the patterns outside the data sets. This will tremendously restrict the applications of deep learning in optical tomography reconstruction. To address this problem, a self-training strategy is proposed for BLT reconstruction in this paper. The proposed strategy can fast generate large-scale BLT data sets with random target numbers, shapes, and sizes through an algorithm named random seed growth algorithm and the neural network is automatically self-trained. In addition, the proposed strategy uses the neural network to build a map between photon densities on surface and inside the imaged object rather than an end-to-end neural network that directly infers the distribution of sources from the photon density on surface. The map of photon density is further converted into the distribution of sources through the multiplication with stiffness matrix. Simulation, phantom, and mouse studies are carried out. Results show the availability of the proposed self-training strategy.

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.

Adaptive permissible region based random Kaczmarz reconstruction method for localization of carotid atherosclerotic plaques in fluorescence molecular tomography

Objective. In this study, we propose the adaptive permissible region based random Kaczmarz method as an improved reconstruction method to recover small carotid atherosclerotic plaque targets in rodents with high resolution in fluorescence molecular tomography (FMT). Approach. We introduce the random Kaczmarz method as an advanced minimization method to solve the FMT inverse problem. To satisfy the special condition of this method, we proposed an adaptive permissible region strategy based on traditional permissible region methods to flexibly compress the dimension of the solution space. Main results. Monte Carlo simulations, phantom experiments, and in vivo experiments demonstrate that the proposed method can recover the small carotid atherosclerotic plaque targets with high resolution and accuracy, and can achieve lower root mean squared error and distance error (DE) than other traditional methods. For targets with 1.5 mm diameter and 0.5 mm separation, the DE indicators can be improved by up to 40%. Moreover, the proposed method can be utilized for in vivo locating atherosclerotic plaques with high accuracy and robustness. Significance. We applied the random Kaczmarz method to solve the inverse problem in FMT and improve the reconstruction result via this advanced minimization method. We verified that the FMT technology has a great potential to locate and quantify atherosclerotic plaques with higher accuracy, and can be expanded to more preclinical research.

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.

Method for improving the accuracy of fluorescence molecular tomography based on multi-wavelength concurrent reconstruction

A Concurrent-wavelength Reconstruction Algorithm (CRA) based on multi-wavelength information fusion is proposed in this paper that aims to further improve the accuracy of Fluorescence Molecular Tomography (FMT) reconstruction. Combining multi-spectral data with FMT technology, the information of 650 and 750 nm wavelengths near-infrared was used to increase the feature information of the dominant 850 nm wavelength near-infrared effectively. Principal component analysis, which can remove redundant information and achieve data dimensionality reduction, was then utilized to extract the feature information. Finally, tomographic reconstruction of the anomalies was performed based on the stacked auto-encoder neural network model. The comparison results of numerical experiments showed that the reconstruction effect of CRA was superior to the performance of the single wavelength model. The correlation coefficient between CRA reconstructed anomalies' fluorescence yield values and the real fluorescence yield values remained at 0.95 or more under the noise of different levels of signal-to-noise ratios. Therefore, the CRA proposed in this paper could effectively improve on the ill-posedness of the inverse problem, which could further enhance the accuracy of FMT reconstruction.

L1-L2 norm regularization via forward-backward splitting for fluorescence molecular tomography

Fluorescent molecular tomography (FMT) is a highly sensitive and noninvasive imaging approach for providing three-dimensional distribution of fluorescent marker probes. However, owing to its light scattering effect and the ill-posedness of inverse problems, it is challenging to develop an efficient reconstruction algorithm that can achieve the exact location and morphology of the fluorescence source. In this study, therefore, in order to satisfy the need for early tumor detection and improve the sparsity of solution, we proposed a novel L ₁-L ₂ norm regularization via the forward-backward splitting method for enhancing the FMT reconstruction accuracy and the robustness. By fully considering the highly coherent nature of the system matrix of FMT, it operates by splitting the objective to be minimized into simpler functions, which are dealt with individually to obtain a sparser solution. An analytic solution of L ₁-L ₂ norm proximal operators and a forward-backward splitting algorithm were employed to efficiently solve the nonconvex L ₁-L ₂ norm minimization problem. Numerical simulations and an in-vivo glioma mouse model experiment were conducted to evaluate the performance of our algorithm. The comparative results of these experiments demonstrated that the proposed algorithm obtained superior reconstruction performance in terms of spatial location, dual-source resolution, and in-vivo practicability. It was believed that this study would promote the preclinical and clinical applications of FMT in early tumor detection.

Attention mechanism-based locally connected network for accurate and stable reconstruction in Cerenkov luminescence tomography

Cerenkov luminescence tomography (CLT) is a novel and highly sensitive imaging technique, which could obtain the three-dimensional distribution of radioactive probes to achieve accurate tumor detection. However, the simplified radiative transfer equation and ill-conditioned inverse problem cause a reconstruction error. In this study, a novel attention mechanism based locally connected (AMLC) network was proposed to reduce barycenter error and improve morphological restorability. The proposed AMLC network consisted of two main parts: a fully connected sub-network for providing a coarse reconstruction result, and a locally connected sub-network based on an attention matrix for refinement. Both numerical simulations and in vivo experiments were conducted to show the superiority of the AMLC network in accuracy and stability over existing methods (MFCNN, KNN-LC network). This method improved CLT reconstruction performance and promoted the application of machine learning in optical imaging research.

Bioluminescence Tomography Based on One-Dimensional Convolutional Neural Networks

Bioluminescent tomography (BLT) has increasingly important applications in preclinical studies. However, the simplified photon propagation model and the inherent ill-posedness of the inverse problem limit the quality of BLT reconstruction. In order to improve the reconstruction accuracy of positioning and reconstruction efficiency, this paper presents a deep-learning optical reconstruction method based on one-dimensional convolutional neural networks (1DCNN). The nonlinear mapping relationship between the surface photon flux density and the distribution of the internal bioluminescence sources is directly established, which fundamentally avoids solving the ill-posed inverse problem iteratively. Compared with the previous reconstruction method based on multilayer perceptron, the training parameters in the 1DCNN are greatly reduced and the learning efficiency of the model is improved. Simulations verify the superiority and stability of the 1DCNN method, and the in vivo experimental results further show the potential of the proposed method in practical applications.

Alternating Direction Method of Multipliers Network for Bioluminescence Tomography Reconstruction

Bioluminescence tomography (BLT) is an effective noninvasive molecular imaging modality for three dimensional visualization of in vivo tumor research in small animals. The approaches of deep learning have shown great potential in the field of optical molecular imaging in recent years. However, the common problem with these existing end-to-end networks is the black box technology, whose solving process is not theoretically proven. In this work, we proposed a novel Alternating Direction Method of Multipliers Network (ADMM-Net) to solve the poor interpretation problem of internal process. The ADMM-Net combines the framework of deep learning on the basis of traditional ADMM algorithm to dynamically learn various parameters of the algorithm in the form of network. To evaluate the performance of our proposed network, we implemented numerical simulation experiments. The results show that the ADMM-Net can accurately reconstruct the location of the source, and the morphological similarity with the real source is also higher.

A review of the application of machine learning in molecular imaging

Molecular imaging (MI) is a science that uses imaging methods to reflect the changes of molecular level in living state and conduct qualitative and quantitative studies on its biological behaviors in imaging. Optical molecular imaging (OMI) and nuclear medical imaging are two key research fields of MI. OMI technology refers to the optical information generated by the imaging target (such as tumors) due to drug intervention and other reasons. By collecting the optical information, researchers can track the motion trajectory of the imaging target at the molecular level. Owing to its high specificity and sensitivity, OMI has been widely used in preclinical research and clinical surgery. Nuclear medical imaging mainly detects ionizing radiation emitted by radioactive substances. It can provide molecular information for early diagnosis, effective treatment and basic research of diseases, which has become one of the frontiers and hot topics in the field of medicine in the world today. Both OMI and nuclear medical imaging technology require a lot of data processing and analysis. In recent years, artificial intelligence technology, especially neural network-based machine learning (ML) technology, has been widely used in MI because of its powerful data processing capability. It provides a feasible strategy to deal with large and complex data for the requirement of MI. In this review, we will focus on the applications of ML methods in OMI and nuclear medical imaging.

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.