Detection of Fatigue Cracks for Concrete Structures by Using Carbon Ink-Based Conductive Skin and Electrical Resistance Tomography

Concrete is among the most widely used structural materials in buildings and bridges all over the world. During their service life, concrete structures may inevitably display cracks due to long-term fatigue loads, leading to the degradation of structural integrity. Thus, it is very important to detect cracks and their growth in concrete structures using an automated structural health monitoring system. In this paper, experimental research on crack detection and imaging of concrete structures by using sensing skin and electrical resistance tomography (ERT) is presented. Carbon ink is screen-printed on the surface of concrete as a conductive material to form sensing skins. With these sensing skins, when cracks occur on or near the surface, it breaks the continuity of the sensing skins and significantly reduces conductivity in cracking areas. Then, after exciting small currents in sensing skins and measuring related voltage data, an inverse analysis based on total variation (TV) regularization is adopted to reconstruct tomographic images showing conductivity changes in sensing skins, to detect the occurrence and growth of cracks. The effectiveness of conductive sensing skins and our related crack detection method is validated in experimental studies on a concrete beam subjected to fatigue tests.

Superresolution structured illumination microscopy reconstruction algorithms: a review

Structured illumination microscopy (SIM) has become the standard for next-generation wide-field microscopy, offering ultrahigh imaging speed, superresolution, a large field-of-view, and long-term imaging. Over the past decade, SIM hardware and software have flourished, leading to successful applications in various biological questions. However, unlocking the full potential of SIM system hardware requires the development of advanced reconstruction algorithms. Here, we introduce the basic theory of two SIM algorithms, namely, optical sectioning SIM (OS-SIM) and superresolution SIM (SR-SIM), and summarize their implementation modalities. We then provide a brief overview of existing OS-SIM processing algorithms and review the development of SR-SIM reconstruction algorithms, focusing primarily on 2D-SIM, 3D-SIM, and blind-SIM. To showcase the state-of-the-art development of SIM systems and assist users in selecting a commercial SIM system for a specific application, we compare the features of representative off-the-shelf SIM systems. Finally, we provide perspectives on the potential future developments of SIM.

3D reconstruction of unstained weakly scattering cells from a single defocused hologram

We investigate the problem of 3D complex field reconstruction corresponding to unstained red blood cells (RBCs) with a single defocused off-axis digital hologram. The main challenge in this problem is the localization of cells to the correct axial range. While investigating the volume recovery problem for a continuous phase object like the RBC, we observe an interesting feature of the backpropagated field that it does not show a clear focusing effect. Therefore, sparsity enforcement within the iterative optimization framework using a single hologram data frame cannot effectively restrict the reconstruction to the true object volume. For phase objects, it is known that the amplitude contrast of the backpropagated object field at the focus plane is minimum. We use this information available in the recovered object field in the hologram plane to device depth-dependent weights that are proportional to the inverse of amplitude contrast. This weight function is employed in the iterative steps of the optimization algorithm to assist the object volume localization. The overall reconstruction process is performed using the mean gradient descent (MGD) framework. Experimental illustrations of 3D volume reconstruction of the healthy as well as malaria-infected RBCs are presented. A test sample of polystyrene microsphere bead is also used to validate the axial localization capability of the proposed iterative technique. The proposed methodology is simple to implement experimentally and provides an approximate tomographic solution, which is axially restricted and consistent with the object field data.

Algorithms and instrumentation for rapid spatial frequency domain fluorescence diffuse optical imaging

SIGNIFICANCE

Rapid estimation of the depth and margins of fluorescence targets buried below the tissue surface could improve upon current image-guided surgery techniques for tumor resection.

AIM

We describe algorithms and instrumentation that permit rapid estimation of the depth and transverse margins of fluorescence target(s) in turbid media; the work aims to introduce, experimentally demonstrate, and characterize the methodology.

APPROACH

Spatial frequency domain fluorescence diffuse optical tomography (SFD-FDOT) technique is adapted for rapid and computationally inexpensive estimation of fluorophore target depth and lateral margins. The algorithm utilizes the variation of diffuse fluorescence intensity with respect to spatial-modulation-frequency to compute target depth. The lateral margins are determined via analytical inversion of the data using depth information obtained from the first step. We characterize method performance using fluorescent contrast targets embedded in tissue-simulating phantoms.

RESULTS

Single and multiple targets with significant lateral size were imaged at varying depths as deep as 1 cm. Phantom data analysis showed good depth-sensitivity, and the reconstructed transverse margins were mostly within ∼30 % error from true margins.

CONCLUSIONS

The study suggests that the rapid SFD-FDOT approach could be useful in resection surgery and, more broadly, as a first step in more rigorous SFD-FDOT reconstructions. The experiments permit evaluation of current limitations.

sCMOS Noise-Corrected Superresolution Reconstruction Algorithm for Structured Illumination Microscopy

Structured illumination microscopy (SIM) is widely applied due to its high temporal and spatial resolution imaging ability. sCMOS cameras are often used in SIM due to their superior sensitivity, resolution, field of view, and frame rates. However, the unique single-pixel-dependent readout noise of sCMOS cameras may lead to SIM reconstruction artefacts and affect the accuracy of subsequent statistical analysis. We first established a nonuniform sCMOS noise model to address this issue, which incorporates the single-pixel-dependent offset, gain, and variance based on the SIM imaging process. The simulation indicates that the sCMOS pixel-dependent readout noise causes artefacts in the reconstructed SIM superresolution (SR) image. Thus, we propose a novel sCMOS noise-corrected SIM reconstruction algorithm derived from the imaging model, which can effectively suppress the sCMOS noise-related reconstruction artefacts and improve the signal-to-noise ratio (SNR).

Ultrasonic Time-of-Flight Computed Tomography for Investigation of Batch Crystallisation Processes

Crystallisation is a crucial step in many industrial processes. Many sensors are being investigated for monitoring such processes to enhance the efficiency of them. Ultrasound techniques have been used for particle sizing characterization of liquid suspensions, in crystallisation process. An ultrasound tomography system with an array of ultrasound sensors can provide spatial information inside the process when compared to single-measurement systems. In this study, the batch crystallisation experiments have been conducted in a lab-scale reactor in calcium carbonate crystallisation. Real-time ultrasound tomographic imaging is done via a contactless ultrasound tomography sensor array. The effect of the injection rate and the stirring speed was considered as two control parameters in these crystallisation functions. Transmission mode ultrasound tomography comprises 32 piezoelectric transducers with central frequency of 40 kHz has been used. The process-based experimental investigation shows the capability of the proposed ultrasound tomography system for crystallisation process monitoring. Information on process dynamics, as well as process malfunction, can be obtained via the ultrasound tomography system.

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.

Domain Transform Network for Photoacoustic Tomography from Limited-view and Sparsely Sampled Data

Medical image reconstruction methods based on deep learning have recently demonstrated powerful performance in photoacoustic tomography (PAT) from limited-view and sparse data. However, because most of these methods must utilize conventional linear reconstruction methods to implement signal-to-image transformations, their performance is restricted. In this paper, we propose a novel deep learning reconstruction approach that integrates appropriate data pre-processing and training strategies. The Feature Projection Network (FPnet) presented herein is designed to learn this signal-to-image transformation through data-driven learning rather than through direct use of linear reconstruction. To further improve reconstruction results, our method integrates an image post-processing network (U-net). Experiments show that the proposed method can achieve high reconstruction quality from limited-view data with sparse measurements. When employing GPU acceleration, this method can achieve a reconstruction speed of 15 frames per second.

Fast and robust reconstruction algorithm for fluorescence diffuse optical tomography assuming a cuboid target

A fast algorithm for fluorescence diffuse optical tomography is proposed. The algorithm is robust against the choice of initial guesses. We estimate the position of a fluorescent target by assuming a cuboid (rectangular parallelepiped) for the fluorophore target. The proposed numerical algorithm is verified by a numerical experiment and an experiment with a meat phantom. The target position is reconstructed with a cuboid from measurements in the time domain. Moreover, the long-time behavior of the emission light is investigated making use of the analytical solution to the diffusion equation.

Limited view cone-beam x-ray luminescence tomography based on depth compensation and group sparsity prior

Significance: As a promising hybrid imaging technique with x-ray excitable nanophosphors, cone-beam x-ray luminescence computed tomography (CB-XLCT) has been proposed for in-depth biological imaging applications. In situations in which the full rotation of the imaging object (or x-ray source) is inapplicable, the x-ray excitation is limited by geometry, or a lower x-ray excitation dose is mandatory, limited view CB-XLCT reconstruction would be essential. However, this will result in severe ill-posedness and poor image quality. <p> Aim: The aim is to develop a limited view CB-XLCT imaging strategy to reduce the scanning span and a corresponding reconstruction method to achieve robust imaging performance.</p> <p> Approach: In this study, a group sparsity-based reconstruction method is proposed with the consideration that nanophosphors usually cluster in certain regions, such as tumors or major organs such as the liver. In addition, depth compensation (DC) is adopted to avoid the depth inconsistency caused by a limited view strategy. </p> <p> Results: Experiments using numerical simulations and physical phantoms with different edge-to-edge distances were carried out to illustrate the validity of the proposed method. The reconstruction results showed that the proposed method outperforms conventional methods in terms of localization accuracy, target shape, image contrast, and spatial resolution with two perpendicular projections. </p> <p> Conclusions: A limited view CB-XLCT imaging strategy with two perpendicular projections and a reconstruction method based on DC and group sparsity, which is essential for fast CB-XLCT imaging and for some practical imaging applications, such as imaging-guided surgery, is proposed. </p>

A Quantitative Ultrasonic Travel-Time Tomography to Investigate Liquid Elaborations in Industrial Processes

This work presents an ultrasound tomography imaging system and method for quantitative mapping of the sound speed in liquid masses. It is highly desirable to be able to inspect vessel fluid mass distribution, notably in the chemical and food industrial operations. Optimization of industrial reactors has been crucial to the improvement of industrial processes. There is a great need to investigate how and if tomographic imaging sensors could aid the automatic control of these process tanks. Single-measurement ultrasound techniques and especially spectrometric methods have been a subject of study of industrial applications. Tomographic systems provide key multi-dimensional and spatial information when compared to the well-established single-channel measurement system. Recently, ultrasound tomography has attracted a great deal of interest in a wide spectrum of industrial applications. The system has been designed as 32 piezoelectric ring-array positioned in a 30 cm tank, with an excitation frequency of 40 kHz. Two-dimensional transmission travel-time tomography was developed to reconstruct the fluid mass distributions. Prior experiments are mainly based on inclusions of a few centimetres and on a liquid solution of different concentrations. They have been conducted to test the spatial and quantitative resolution of the ultrasound imaging device. Analysing the reconstructed images, it is possible to provide accurate spatial resolution with low position errors. The system also demonstrated inclusion movement with a temporal resolution of 4 frames per second (fps) in dynamical imaging sense. Sound velocity quantitative imaging was developed for the investigation of ultrasonic propagation in different liquids. This work, for the first time, shows how quantitative sound velocity imaging using transmission mode time of flight data could be used to characterize liquid density distribution of industrial reactors. The results suggest that ultrasound tomography can be used to quantitatively monitor important process parameters.

BM3D-based total variation algorithm for speckle removal with structure-preserving in OCT images

In this paper, we propose a total variation based on block matching 3D (BM3D-TV method), which includes the total variation regular term, the data fidelity term, and the block matching term. In addition, we also propose a fast numerical algorithm based on the split Bregman iteration for the proposed method. By assigning suitable weights to the data fidelity term and block matching term, the image noise reduction and the image structural characteristics can be matched optimally. We test the proposed method on six human retinal and one mouse skin optical coherence tomography (OCT) images respectively, and also compare it with total variation (TV) and BM3D, which were proved to be effective in denoising. The performances of these methods are quantitatively evaluated in terms of the signal-to-noise ratio, the contrast-to-noise ratio, and the averaged equivalent number of homogeneous areas at the aspects of speckle reduction and structure protection. Vast experiments show that the BM3D-TV method can effectively reduce speckle noise in OCT images, protect important structural information and improve image quality, compared with the BM3D and TV methods.

Monitoring Surface Defects Deformations and Displacements in Hot Steel Using Magnetic Induction Tomography

Magnetic Induction Tomography (MIT) is a non-invasive imaging technique that has been widely applied for imaging materials with high electrical conductivity contrasts. Steel production is among an increasing number of applications that require a contactless method for monitoring the casting process due to the high temperature of hot steel. In this paper, an MIT technique is proposed for detecting defects and deformations in the external surfaces of metal, which has the potential to be used to monitor the external surface of hot steel during the continuous casting process. The Total Variation (TV) reconstruction algorithm was developed to image the conductivity distributions. Nonetheless, the reconstructed image of the deformed square metal obtained using the TV algorithm directly does not yield resonable images of the surface deformation. However, differential images obtained by subtracting the image of a perfect square metal with no deformations from the image obtained for a deformed square metal does provide accurate and repeatable deformation information. It is possible to obtain a more precise image of surface deformation by thresholding the differential image. This TV-based threshold-differencing method has been analysed and verified from both simulation and experimental tests. The simulation results reported that 0.92% of the image region can be detected, and the experimental results indicated a 0.57% detectability. Use of the proposed method was demonstareted in a MIT device which was used in continuous casting set up. The paper shows results from computer simulation, lab based cold tests, and real life data from continoeus cating demonstating the effectiveness of the proposed method.

One-step deconvolution for multi-angle TIRF microscopy with enhanced resolution

Total internal reflection fluorescence microscopy (TIRF microscopy) uses a rapid decay of evanescent waves to excite fluorophores within several hundred nanometers (nm) beneath the plasma membrane, which can effectively suppress excitation of fluorescence signals in the deep layers. From image stacks obtained with a plurality of different incident angles, a three-dimensional spatial structure of the observed sample can be reconstructed by a Multi-Angle-TIRF (MA-TIRF) algorithm that provides an axial resolution of ~50 nm. Taking into account the point spread function (PSF) of the TIRF microscopes, we further increase its lateral resolution by introducing a fast deconvolution algorithm into the reconstruction of MA-TIRF data (DMA-TIRF), which is approached in just one step of minimizing the reconstruction function. We also introduce a TV regularization term in the deconvolution algorithm to suppress artifacts induced by the excessive noise. Therefore, based on the hardware of existing MA-TIRF microscopes, the proposed DMA-TIRF algorithm has achieved lateral and axial resolutions of ~200 and ~50 nm, respectively.

Incorporation of Prior Knowledge of Signal Behavior Into the Reconstruction to Accelerate the Acquisition of Diffusion MRI Data

Diffusion MRI data are generally acquired using hyperpolarized gases during patient breath-hold, which yields a compromise between achievable image resolution, lung coverage, and number of -values. In this paper, we propose a novel method that accelerates the acquisition of diffusion MRI data by undersampling in both the spatial and -value dimensions and incorporating knowledge about signal decay into the reconstruction (SIDER). SIDER is compared with total variation (TV) reconstruction by assessing its effect on both the recovery of ventilation images and the estimated mean alveolar dimensions (MADs). Both methods are assessed by retrospectively undersampling diffusion data sets ( =8) of healthy volunteers and patients with Chronic Obstructive Pulmonary Disease (COPD) for acceleration factors between x2 and x10. TV led to large errors and artifacts for acceleration factors equal to or larger than x5. SIDER improved TV, with a lower solution error and MAD histograms closer to those obtained from fully sampled data for acceleration factors up to x10. SIDER preserved image quality at all acceleration factors, although images were slightly smoothed and some details were lost at x10. In conclusion, we developed and validated a novel compressed sensing method for lung MRI imaging and achieved high acceleration factors, which can be used to increase the amount of data acquired during breath-hold. This methodology is expected to improve the accuracy of estimated lung microstructure dimensions and provide more options in the study of lung diseases with MRI.

Exploitation of temporal redundancy in compressed sensing reconstruction of fMRI studies with a prior-based algorithm (PICCS)

PURPOSE

Compressed sensing is a technique used to accelerate magnetic resonance imaging (MRI) acquisition without compromising image quality. While it has proven particularly useful in dynamic imaging procedures such as cardiac cine, very few authors have applied it to functional magnetic resonance imaging (fMRI). The purpose of the present study was to check whether the prior image constrained compressed sensing (PICCS) algorithm, which is based on an available prior image, can improve the statistical maps in fMRI better than other strategies that also exploit temporal redundancy.

METHODS

PICCS was compared to spatiotemporal total variation (TTV) and k-t FASTER, since they have already demonstrated high performance and robustness in other MRI applications, such as cardiac cine MRI and resting state fMRI, respectively. The prior image for PICCS was the average of all undersampled data. Both PICCS and TTV were solved using the split Bregman formulation. K-t FASTER algorithm relies on matrix completion to reconstruct the undersampled k-spaces. The three algorithms were evaluated using two datasets with high and low signal-to-noise ratio (SNR)-BOLD contrast-acquired in a 7 T preclinical MRI scanner and retrospectively undersampled at various rates (i.e., acceleration factors). The authors evaluated their performance in terms of the sensitivity/specificity of BOLD detection through receiver operating characteristic curves and by visual inspection of the statistical maps.

RESULTS

With high SNR studies, PICCS performed similarly to the state-of-the-art algorithms TTV and k-t FASTER and provided consistent BOLD signal at the ROI. In scenarios with low SNR and high acceleration factors, PICCS still provided consistent maps and higher sensitivity/specificity than TTV, whereas k-t FASTER failed to provide significant maps.

CONCLUSIONS

The authors performed a comparison between three reconstructions (PICCS, TTV, and k-t FASTER) that exploit temporal redundancy in fMRI. The prior-based algorithm, PICCS, preserved BOLD activation and sensitivity/specificity better than TTV and k-t FASTER in noisy scenarios. The PICCS algorithm can potentially reach an acceleration factor of ×8 and still provide BOLD contrast in the ROI with an area under the curve over 0.99.

A Novel Prior- and Motion-Based Compressed Sensing Method for Small-Animal Respiratory Gated CT

Low-dose protocols for respiratory gating in cardiothoracic small-animal imaging lead to streak artifacts in the images reconstructed with a Feldkamp-Davis-Kress (FDK) method. We propose a novel prior- and motion-based reconstruction (PRIMOR) method, which improves prior-based reconstruction (PBR) by adding a penalty function that includes a model of motion. The prior image is generated as the average of all the respiratory gates, reconstructed with FDK. Motion between respiratory gates is estimated using a nonrigid registration method based on hierarchical B-splines. We compare PRIMOR with an equivalent PBR method without motion estimation using as reference the reconstruction of high dose data. From these data acquired with a micro-CT scanner, different scenarios were simulated by changing photon flux and number of projections. Methods were evaluated in terms of contrast-to-noise-ratio (CNR), mean square error (MSE), streak artefact indicator (SAI), solution error norm (SEN), and correction of respiratory motion. Also, to evaluate the effect of each method on lung studies quantification, we have computed the Jaccard similarity index of the mask obtained from segmenting each image as compared to those obtained from the high dose reconstruction. Both iterative methods greatly improved FDK reconstruction in all cases. PBR was prone to streak artifacts and presented blurring effects in bone and lung tissues when using both a low number of projections and low dose. Adopting PBR as a reference, PRIMOR increased CNR up to 33% and decreased MSE, SAI and SEN up to 20%, 4% and 13%, respectively. PRIMOR also presented better compensation for respiratory motion and higher Jaccard similarity index. In conclusion, the new method proposed for low-dose respiratory gating in small-animal scanners shows an improvement in image quality and allows a reduction of dose or a reduction of the number of projections between two and three times with respect to previous PBR approaches.

Fast multislice fluorescence molecular tomography using sparsity-inducing regularization

Fluorescence molecular tomography (FMT) is a rapidly growing imaging method that facilitates the recovery of small fluorescent targets within biological tissue. The major challenge facing the FMT reconstruction method is the ill-posed nature of the inverse problem. In order to overcome this problem, the acquisition of large FMT datasets and the utilization of a fast FMT reconstruction algorithm with sparsity regularization have been suggested recently. Therefore, the use of a joint L1/total-variation (TV) regularization as a means of solving the ill-posed FMT inverse problem is proposed. A comparative quantified analysis of regularization methods based on L1-norm and TV are performed using simulated datasets, and the results show that the fast composite splitting algorithm regularization method can ensure the accuracy and robustness of the FMT reconstruction. The feasibility of the proposed method is evaluated in an in vivo scenario for the subcutaneous implantation of a fluorescent-dye-filled capillary tube in a mouse, and also using hybrid FMT and x-ray computed tomography data. The results show that the proposed regularization overcomes the difficulties created by the ill-posed inverse problem.

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.

Nonlinear approach to difference imaging in diffuse optical tomography

Difference imaging aims at recovery of the change in the optical properties of a body based on measurements before and after the change. Conventionally, the image reconstruction is based on using difference of the measurements and a linear approximation of the observation model. One of the main benefits of the linearized difference reconstruction is that the approach has a good tolerance to modeling errors, which cancel out partially in the subtraction of the measurements. However, a drawback of the approach is that the difference images are usually only qualitative in nature and their spatial resolution can be weak because they rely on the global linearization of the nonlinear observation model. To overcome the limitations of the linear approach, we investigate a nonlinear approach for difference imaging where the images of the optical parameters before and after the change are reconstructed simultaneously based on the two datasets. We tested the feasibility of the method with simulations and experimental data from a phantom and studied how the approach tolerates modeling errors like domain truncation, optode coupling errors, and domain shape errors.

X-ray luminescence computed tomography imaging based on X-ray distribution model and adaptively split Bregman method

X-ray luminescence computed tomography (XLCT) has become a promising imaging technology for biological application based on phosphor nanoparticles. There are mainly three kinds of XLCT imaging systems: pencil beam XLCT, narrow beam XLCT and cone beam XLCT. Narrow beam XLCT can be regarded as a balance between the pencil beam mode and the cone-beam mode in terms of imaging efficiency and image quality. The collimated X-ray beams are assumed to be parallel ones in the traditional narrow beam XLCT. However, we observe that the cone beam X-rays are collimated into X-ray beams with fan-shaped broadening instead of parallel ones in our prototype narrow beam XLCT. Hence we incorporate the distribution of the X-ray beams in the physical model and collected the optical data from only two perpendicular directions to further speed up the scanning time. Meanwhile we propose a depth related adaptive regularized split Bregman (DARSB) method in reconstruction. The simulation experiments show that the proposed physical model and method can achieve better results in the location error, dice coefficient, mean square error and the intensity error than the traditional split Bregman method and validate the feasibility of method. The phantom experiment can obtain the location error less than 1.1 mm and validate that the incorporation of fan-shaped X-ray beams in our model can achieve better results than the parallel X-rays.

Comparative study of iterative reconstruction algorithms for missing cone problems in optical diffraction tomography

In optical tomography, there exist certain spatial frequency components that cannot be measured due to the limited projection angles imposed by the numerical aperture of objective lenses. This limitation, often called as the missing cone problem, causes the under-estimation of refractive index (RI) values in tomograms and results in severe elongations of RI distributions along the optical axis. To address this missing cone problem, several iterative reconstruction algorithms have been introduced exploiting prior knowledge such as positivity in RI differences or edges of samples. In this paper, various existing iterative reconstruction algorithms are systematically compared for mitigating the missing cone problem in optical diffraction tomography. In particular, three representative regularization schemes, edge preserving, total variation regularization, and the Gerchberg-Papoulis algorithm, were numerically and experimentally evaluated using spherical beads as well as real biological samples; human red blood cells and hepatocyte cells. Our work will provide important guidelines for choosing the appropriate regularization in ODT.

Investigation of different sparsity transforms for the PICCS algorithm in small-animal respiratory gated CT

Respiratory gating helps to overcome the problem of breathing motion in cardiothoracic small-animal imaging by acquiring multiple images for each projection angle and then assigning projections to different phases. When this approach is used with a dose similar to that of a static acquisition, a low number of noisy projections are available for the reconstruction of each respiratory phase, thus leading to streak artifacts in the reconstructed images. This problem can be alleviated using a prior image constrained compressed sensing (PICCS) algorithm, which enables accurate reconstruction of highly undersampled data when a prior image is available. We compared variants of the PICCS algorithm with different transforms in the prior penalty function: gradient, unitary, and wavelet transform. In all cases the problem was solved using the Split Bregman approach, which is efficient for convex constrained optimization. The algorithms were evaluated using simulations generated from data previously acquired on a micro-CT scanner following a high-dose protocol (four times the dose of a standard static protocol). The resulting data were used to simulate scenarios with different dose levels and numbers of projections. All compressed sensing methods performed very similarly in terms of noise, spatiotemporal resolution, and streak reduction, and filtered back-projection was greatly improved. Nevertheless, the wavelet domain was found to be less prone to patchy cartoon-like artifacts than the commonly used gradient domain.

Comparison of total variation with a motion estimation based compressed sensing approach for self-gated cardiac cine MRI in small animal studies

Purpose

Compressed sensing (CS) has been widely applied to prospective cardiac cine MRI. The aim of this work is to study the benefits obtained by including motion estimation in the CS framework for small-animal retrospective cardiac cine.

Methods

We propose a novel B-spline-based compressed sensing method (SPLICS) that includes motion estimation and generalizes previous spatiotemporal total variation (ST-TV) methods by taking into account motion between frames. In addition, we assess the effect of an optimum weighting between spatial and temporal sparsity to further improve results. Both methods were implemented using the efficient Split Bregman methodology and were evaluated on rat data comparing animals with myocardial infarction with controls for several acceleration factors.

Results

ST-TV with optimum selection of the weighting sparsity parameter led to results similar to those of SPLICS; ST-TV with large relative temporal sparsity led to temporal blurring effects. However, SPLICS always properly corrected temporal blurring, independently of the weighting parameter. At acceleration factors of 15, SPLICS did not distort temporal intensity information but led to some artefacts and slight over-smoothing. At an acceleration factor of 7, images were reconstructed without significant loss of quality.

Conclusion

We have validated SPLICS for retrospective cardiac cine in small animal, achieving high acceleration factors. In addition, we have shown that motion modelling may not be essential for retrospective cine and that similar results can be obtained by using ST-TV provided that an optimum selection of the spatiotemporal sparsity weighting parameter is performed.

Reweighted L1 regularization for restraining artifacts in FMT reconstruction images with limited measurements

In fluorescence molecular tomography (FMT), many artifacts exist in the reconstructed images because of the inherently ill-posed nature of the FMT inverse problem, especially with limited measurements. A new method based on iterative reweighted L1 (IRL1) regularization is proposed for reducing artifacts with limited measurements. Phantom experiments demonstrate that the reconstructed images have fewer artifacts even with very limited measurements. This indicates that FMT based on IRL1 can obtain high-quality images and thus has the potential to observe dynamic changes in fluorescence-targeted molecules.

MAP estimation with structural priors for fluorescence molecular tomography

Fluorescence molecular tomography (FMT) is an attractive imaging tool for quantitatively and three-dimensionally resolving fluorophore distributions in small animals, but it suffers from low spatial resolution due to its inherent ill-posed nature. Structural priors obtained from a secondary modality system such as x-ray computed tomography or magnetic resonance imaging can help to improve FMT reconstruction results. However, challenge remains in how to fully take advantage of the structural priors while effectively avoid undesirable influence caused by an immoderate usage. In this paper, we propose a new method to resolve the FMT inverse problem based on maximum a posteriori (MAP) estimation with structural priors (MAP-SP) in a Bayesian framework. Instead of imposing the structural priors directly on the reconstruction results, the MAP-SP method utilizes them to constrain the unknown hyperparameters of the prior information model which is essential for the Bayesian framework. Then, a low dimensional inverse problem and an alternating optimization scheme are used to automatically calculate the unknown hyperparameters, which make the FMT reconstruction process self-adaptive. Simulation and phantom results show that the proposed MAP-SP method can effectively make use of the structural priors and leads to improvements in reconstruction quality as compared with traditional regularization methods.