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

Fluorescence molecular tomography based on an online maximum a posteriori estimation algorithm

Fluorescence molecular tomography (FMT) is a non-invasive, radiation-free, and highly sensitive optical molecular imaging technique for early tumor detection. However, inadequate measurement information along with significant scattering of near-infrared light within the tissue leads to high ill-posedness in the inverse problem of FMT. To improve the quality and efficiency of FMT reconstruction, we build a reconstruction model based on log-sum regularization and introduce an online maximum a posteriori estimation (OPE) algorithm to solve the non-convex optimization problem. The OPE algorithm approximates a stationary point by evaluating the gradient of the objective function at each iteration, and its notable strength lies in the remarkable speed of convergence. The results of simulations and experiments demonstrate that the OPE algorithm ensures good reconstruction quality and exhibits outstanding performance in terms of reconstruction efficiency.

Two-step reconstruction framework of fluorescence molecular tomography based on energy statistical probability

Fluorescence molecular tomography (FMT), as a promising technique for early tumor detection, can non-invasively visualize the distribution of fluorescent marker probe three-dimensionally. However, FMT reconstruction is a severely ill-posed problem, which remains an obstacle to wider application of FMT. In this paper, a two-step reconstruction framework was proposed for FMT based on the energy statistical probability. First, the tissue structural information obtained from computed tomography (CT) is employed to associate the tissue optical parameters for rough solution in the global region. Then, according to the global-region reconstruction results, the probability that the target belongs to each region can be calculated. The region with the highest probability is delineated as region of interest to realize accurate and fast source reconstruction. Numerical simulations and in vivo experiments were carried out to evaluate the effectiveness of the proposed framework. The encouraging results demonstrate the significant effectiveness and potential of our method for practical FMT applications.

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.

Multi-target reconstruction strategy based on blind source separation of surface measurement signals in FMT

Fluorescence molecular tomography (FMT) is a promising molecular imaging technique for tumor detection in the early stage. High-precision multi-target reconstructions are necessary for quantitative analysis in practical FMT applications. The existing reconstruction methods perform well in retrieving a single fluorescent target but may fail in reconstructing a multi-target, which remains an obstacle to the wider application of FMT. In this paper, a novel multi-target reconstruction strategy based on blind source separation (BSS) of surface measurement signals was proposed, which transformed the multi-target reconstruction problem into multiple single-target reconstruction problems. Firstly, by multiple points excitation, multiple groups of superimposed measurement signals conforming to the conditions of BSS were constructed. Secondly, an efficient nonnegative least-correlated component analysis with iterative volume maximization (nLCA-IVM) algorithm was applied to construct the separation matrix, and the superimposed measurement signals were separated into the measurements of each target. Thirdly, the least squares fitting method was combined with BSS to determine the number of fluorophores indirectly. Lastly, each target was reconstructed based on the extracted surface measurement signals. Numerical simulations and in vivo experiments proved that it has the ability of multi-target resolution for FMT. The encouraging results demonstrate the significant effectiveness and potential of our method for practical FMT applications.

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.

Accurate and fast reconstruction for bioluminescence tomography based on adaptive Newton hard thresholding pursuit algorithm

As a promising noninvasive medical imaging technique, bioluminescence tomography (BLT) dynamically offers three-dimensional visualization of tumor distribution in living animals. However, due to the high ill-posedness caused by the strong scattering property of biological tissues and the limited boundary measurements with noise, BLT reconstruction still cannot meet actual preliminary clinical application requirements. In our research, to recover 3D tumor distribution quickly and precisely, an adaptive Newton hard thresholding pursuit (ANHTP) algorithm is proposed to improve the performance of BLT. The ANHTP algorithm fully combines the advantages of sparsity constrained optimization and convex optimization to guarantee global convergence. More precisely, an adaptive sparsity adjustment strategy was developed to obtain the support set of the inverse system matrix. Based on the strong Wolfe line search criterion, a modified damped Newton algorithm was constructed to obtain optimal source distribution information. A series of numerical simulations and phantom and in vivo experiments show that ANHTP has high reconstruction accuracy, fast reconstruction speed, and good robustness. Our proposed algorithm can further increase the practicality of BLT in biomedical applications.

L1-L2 Minimization Via A Proximal Operator For Fluorescence Molecular Tomography

Fluorescent Molecular Tomography (FMT) is a highly sensitive and noninvasive imaging method that provides three-dimensional distribution of biomarkers by noninvasive detection of fluorescent marker probes. However, due to the light scattering effect and ill-posedness of inverse problems, it is challenging to develop an efficient construction method that can provide the exact location and morphology of the fluorescence distribution. In this paper, we proposed L₁-L₂ norm regularization to improve FMT reconstruction. In our research, proximal operators of non-convex L₁ -L₂ norm and forward-backward splitting method was adopted to solve the inverse problem of FMT. Simulation results on heterogeneous mouse model demonstrated that the proposed FBS method is superior to IVTCG, DCA and IRW-L_1/2 reconstruction methods in location accuracy and other aspects.

A robust elastic net-ℓ1ℓ2reconstruction method for x-ray luminescence computed tomography

Objective. X-ray luminescence computed tomography (XLCT) has played a crucial role in pre-clinical research and effective diagnosis of disease. However, due to the ill-posed of the XLCT inverse problem, the generalization of reconstruction methods and the selection of appropriate regularization parameters are still challenging in practical applications. In this research, an robust Elastic net-ℓ₁ℓ₂reconstruction method is proposed aiming to the challenge.Approach. Firstly, our approach consists of ℓ₁and ℓ₂regularization to enhance the sparsity and suppress the smoothness. Secondly, through optimal approximation of the optimization problem, double modification of Landweber algorithm is adopted to solve the Elastic net-ℓ₁ℓ₂regulazation. Thirdly, drawing on the ideal of supervised learning, multi-parameter K-fold cross validation strategy is proposed to determin the optimal parameters adaptively.Main results. To evaluate the performance of the Elastic net-ℓ₁ℓ₂method, numerical simulations, phantom and in vivo experiments were conducted. In these experiments, the Elastic net-ℓ₁ℓ₂method achieved the minimum reconstruction error (with smallest location error, fluorescent yield relative error, normalized root-mean-square error) and the best image reconstruction quality (with largest contrast-to-noise ratio and Dice similarity) among all methods. The results demonstrated that Elastic net-ℓ₁ℓ₂can obtain superior reconstruction performance in terms of location accuracy, dual source resolution, robustness and in vivo practicability.Significance. It is believed that this study will further benefit preclinical applications with a view to provide a more reliable reference for the later researches on XLCT.

Three-term conjugate gradient method for X-ray luminescence computed tomography

X-ray luminescence computed tomography (XLCT) has become an emerging hybrid molecular imaging technology with high detection sensitivity and low cost. However, the inverse problem of reconstruction has severe ill-posed consequences. The original regularization algorithm needs to take much time to solve the problem. To reduce the cost of time, a three-term conjugate gradient (TTCG) algorithm is proposed for XLCT. Useful truncation information is added to the descent direction to find the optimal solution quickly in our proposed algorithm. Both numerical simulation experiments and real experiments are carried out to verify the performance of the algorithm. Experimental results show that the presented algorithm can effectively speed up the reconstruction process.

Nonconvex Laplacian Manifold Joint Method for Morphological Reconstruction of Fluorescence Molecular Tomography

PURPOSE

Fluorescence molecular tomography (FMT) is a promising technique for three-dimensional (3D) visualization of biomarkers in small animals. Morphological reconstruction is valuable and necessary for further applications of FMT owing to its innate requirement for knowledge of the molecular probe distributions.

PROCEDURES

In this study, a Laplacian manifold regularization joint ℓ_1/2-norm model is proposed for morphological reconstruction and solved by a nonconvex algorithm commonly referred to as the half-threshold algorithm. The model is combined with the structural and sparsity priors to achieve the location and structure of the target. In addition, two improvement forms (truncated and hybrid truncated forms) are proposed for better morphological reconstruction. The truncated form is proposed for balancing the sharpness and smoothness of the boundary of reconstruction. A hybrid truncated form is proposed for more structural priors. To evaluate the proposed methods, three simulation studies (morphological, robust, and double target analyses) and an in vivo experiment were performed.

RESULTS

The proposed methods demonstrated morphological accuracy, location accuracy, and reconstruction robustness in glioma simulation studies. An in vivo experiment with an orthotopic glioma mouse model confirmed the advantages of the proposed methods. The proposed methods always yielded the best intersection of union (IoU) in simulations and in vivo experiments (mean of 0.80 IoU).

CONCLUSIONS

Simulation studies and in vivo experiments demonstrate that the proposed half-threshold hybrid truncated Laplacian algorithm had an improved performance compared with the comparative algorithm in terms of morphology.

Sparse-graph manifold learning method for bioluminescence tomography

In preclinical researches, bioluminescence tomography (BLT) has widely been used for tumor imaging and monitoring, imaged-guided tumor therapy, and so forth. For these biological applications, both tumor spatial location and morphology analysis are the leading problems needed to be taken into account. However, most existing BLT reconstruction methods were proposed for some specific applications with a focus on sparse representation or morphology recovery, respectively. How to design a versatile algorithm that can simultaneously deal with both aspects remains an impending problem. In this study, a Sparse-Graph Manifold Learning (SGML) method was proposed to balance the source sparseness and morphology, by integrating non-convex sparsity constraint and dynamic Laplacian graph model. Furthermore, based on the nonconvex optimization theory and some iterative approximation, we proposed a novel iteratively reweighted soft thresholding algorithm (IRSTA) to solve the SGML model. Numerical simulations and in vivo experiments result demonstrated that the proposed SGML method performed much superior to the comparative methods in spatial localization and tumor morphology recovery for various source settings. It is believed that the SGML method can be applied to the related optical tomography and facilitate the development of optical molecular tomography.

Fluorescence Molecular Tomography Based on Group Sparsity Priori for Morphological Reconstruction of Glioma

OBJECTIVE

Fluorescence molecular tomography (FMT) is an important tool for life science, which can noninvasive real-time three-dimensional (3-D) visualization for fluorescence source location. FMT is widely used in tumor research due to its high-sensitive and low cost. However, the reconstruction of FMT is difficult. Although the reconstruction methods of FMT have developed rapidly in recent years, the morphological reconstruction of FMT is still a challenge problem. Thus, the purpose of this study is to realize the morphological reconstruction performance of FMT in glioma research.

METHODS

In this study, group sparsity was used as a new priori information for FMT. Besides sparsity, group sparsity also takes the group structure of the fluorescent sources, which can maintain the morphological information of the sources. Fused LASSO method (FLM) was proved it can efficiently model the group sparsity prior. Thus, we utilize FLM to reconstruct the morphological information of glioma. Furthermore, to reduce the influence of the high scattering of skull, we modified the FLM for improving the accuracy of morphological reconstruction.

RESULTS

Glioma numerical simulation model and in vivo glioma model were established to evaluate the performance of morphological reconstruction of the proposed method. The results demonstrated that the proposed method was efficient to reconstruct the morphological information of glioma.

CONCLUSION

Group sparsity priori can effectively improve the morphological accuracy of FMT reconstruction.

SIGNIFICANCE

Group sparsity can maintain the morphological information of fluorescent sources effectively, which has great application potential in FMT. The group sparsity based methods can realize the morphological reconstruction, which is of great practical significance in tumor research.

Sparsity-regularized approaches to directly reconstructing hemodynamic response in brain functional diffuse optical tomography

In brain functional diffuse optical tomography, conventional indirect approaches first separately reconstruct the spatial changes in the absorption coefficients at every time point and then calculate the spatial excited levels in terms of hemodynamic models. Direct approaches combine the two steps necessary in the indirect approaches and obtain the spatial excited levels directly. Although reconstruction quality has been improved by the direct approaches to some extent, they still lack sharp edges and suffer from low spatial resolution because of the ill-posedness of the inverse problems. In this paper, a priori sparsity is introduced to obtain the sparse solutions and further improve reconstruction quality. Simulation experiments are conducted to illustrate the expected performance improvements of the proposed approaches.

Half Thresholding Pursuit Algorithm for Fluorescence Molecular Tomography

OBJECTIVE

Fluorescence Molecular Tomography (FMT) is a promising optical tool for small animal imaging. The l_1/2-norm regularization has attracted attention in the field of FMT due to its ability in enhancing sparsity of solution and coping with the high ill-posedness of the inverse problem. However, efficient algorithm for solving the nonconvex regularized model deserve to explore.

METHOD

A Half Thresholding Pursuit Algorithm (HTPA) combined with parameter optimization is proposed in this paper to efficiently solve the nonconvex optimization model. Specifically, the half thresholding iteration method is utilized to solve l_1/2-norm model, pursuit strategy is used to accelerate the process of iteration, and the parameter optimization scheme is designed to obtain robust parameter.

RESULTS

Analysis and assessment on simulated and experimental data demonstrate that the proposed HTPA performs better in location accuracy and reconstructed fluorescent yield in less time cost, compared with the state-of-the-art reconstruction algorithms.

CONCLUSION

The proposed HTPA combined with the parameter optimization scheme is an efficient and robust reconstruction approach to FMT.

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.

Signal-to-noise ratio analysis and improvement for fluorescence tomography imaging

CCD-based fluorescence tomography is widely used for small animal whole-body imaging. In this report, systematic signal-to-noise ratio (SNR) analyses of a fluorescence tomography imaging (FTI) system were performed, resulting in an easy-to-follow strategy to optimize hardware configurations and operational conditions for acquiring high-quality imaging data and for improving the overall system performance. Phantom experiments were conducted to demonstrate the performance improvement by these optimizations. The improved performance was further verified by imaging a tumor-bearing mouse in vivo. This report provides general and practical guidelines for setting up a high-performance electron multiplying charge coupled device based FTI system to achieve an optimized SNR, which can be useful for future FTI technology development.

Filtered maximum likelihood expectation maximization based global reconstruction for bioluminescence tomography

The reconstruction of bioluminescence tomography (BLT) is severely ill-posed due to the insufficient measurements and diffuses nature of the light propagation. Predefined permissible source region (PSR) combined with regularization terms is one common strategy to reduce such ill-posedness. However, the region of PSR is usually hard to determine and can be easily affected by subjective consciousness. Hence, we theoretically developed a filtered maximum likelihood expectation maximization (fMLEM) method for BLT. Our method can avoid predefining the PSR and provide a robust and accurate result for global reconstruction. In the method, the simplified spherical harmonics approximation (SP_N) was applied to characterize diffuse light propagation in medium, and the statistical estimation-based MLEM algorithm combined with a filter function was used to solve the inverse problem. We systematically demonstrated the performance of our method by the regular geometry- and digital mouse-based simulations and a liver cancer-based in vivo experiment. Graphical abstract The filtered MLEM-based global reconstruction method for BLT.

A hybrid clustering algorithm for multiple-source resolving in bioluminescence tomography

Bioluminescence tomography is a preclinical imaging modality to locate and quantify internal bioluminescent sources from surface measurements, which experienced rapid growth in the last 10 years. However, multiple-source resolving remains a challenging issue in BLT. In this study, it is treated as an unsupervised pattern recognition problem based on the reconstruction result, and a novel hybrid clustering algorithm combining the advantages of affinity propagation (AP) and K-means is developed to identify multiple sources automatically. Moreover, we incorporate the clustering analysis into a general multiple-source reconstruction framework, which can provide stable reconstruction and accurate resolving result without providing the number of targets. Numerical simulations and in vivo experiments on 4T1-luc2 mouse model were conducted to assess the performance of the proposed method in multiple-source resolving. The encouraging results demonstrate significant effectiveness and potential of our method in preclinical BLT applications.

Adaptive threshold method for recovered images of FMT

This paper proposes a post-processing strategy for recovered images of fluorescence molecular tomography. A threshold value is adaptively obtained from the recovered images without external interference, which is objective because it is extracted from the reconstructed result. The recovered images from simulation experiments and physical phantom experiments are processed by this threshold method. And by visualization, the processed images are clearer than those with no post-processing. The full width at half-maximum and contrast-to-noise ratio are then utilized to further verify the effectiveness of the post-processing method, being capable of removing spurious information from the original images, thus bringing convenience to users.

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.

Molecular Imaging of Acute Cardiac Transplant Rejection: Animal Experiments and Prospects

Acute rejection (AR) remains the biggest challenge during the first year after heart transplantation despite advances in immunosuppressive therapy. The early detection and curbing of AR are crucial to the survival of transplant recipients. However, as the criterion standard for AR, endomyocardial biopsy has several limitations because of its inherent invasiveness and morbidity. Traditional imaging techniques, such as echocardiography and cardiac magnetic resonance imaging, are of certain value for AR, but their diagnostic criteria and accuracy remain in question. Molecular imaging sheds new light on AR diagnosis because it can provide information about gene expression and the location of molecules and cells. This article reviews the latest research and applications of several typical modalities of molecular imaging used in AR and discusses their advantages and disadvantages.

Weight Multispectral Reconstruction Strategy for Enhanced Reconstruction Accuracy and Stability With Cerenkov Luminescence Tomography

Cerenkov luminescence tomography (CLT) provides a novel technique for 3-D noninvasive detection of radiopharmaceuticals in living subjects. However, because of the severe scattering of Cerenkov light, the reconstruction accuracy and stability of CLT is still unsatisfied. In this paper, a modified weight multispectral CLT (wmCLT) reconstruction strategy was developed which split the Cerenkov radiation spectrum into several sub-spectral bands and weighted the sub-spectral results to obtain the final result. To better evaluate the property of the wmCLT reconstruction strategy in terms of accuracy, stability and practicability, several numerical simulation experiments and in vivo experiments were conducted and the results obtained were compared with the traditional multispectral CLT (mCLT) and hybrid-spectral CLT (hCLT) reconstruction strategies. The numerical simulation results indicated that wmCLT strategy significantly improved the accuracy of Cerenkov source localization and intensity quantitation and exhibited good stability in suppressing noise in numerical simulation experiments. And the comparison of the results achieved from different in vivo experiments further indicated significant improvement of the wmCLT strategy in terms of the shape recovery of the bladder and the spatial resolution of imaging xenograft tumors. Overall the strategy reported here will facilitate the development of nuclear and optical molecular tomography in theoretical study.

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.

An Lp (0 ≤ p ≤ 1)-norm regularized image reconstruction scheme for breast DOT with non-negative-constraint

Background

In diffuse optical tomography (DOT), the image reconstruction is often an ill-posed inverse problem, which is even more severe for breast DOT since there are considerably increasing unknowns to reconstruct with regard to the achievable number of measurements. One common way to address this ill-posedness is to introduce various regularization methods. There has been extensive research regarding constructing and optimizing objective functions. However, although these algorithms dramatically improved reconstruction images, few of them have designed an essentially differentiable objective function whose full gradient is easy to obtain to accelerate the optimization process.

Methods

This paper introduces a new kind of non-negative prior information, designing differentiable objective functions for cases of L₁-norm, L_p (0 < p < 1)-norm and L₀-norm. Incorporating this non-negative prior information, it is easy to obtain the gradient of these differentiable objective functions, which is useful to guide the optimization process.

Results

Performance analyses are conducted using both numerical and phantom experiments. In terms of spatial resolution, quantitativeness, gray resolution and execution time, the proposed methods perform better than the conventional regularization methods without this non-negative prior information.

Conclusions

The proposed methods improves the reconstruction images using the introduced non-negative prior information. Furthermore, the non-negative constraint facilitates the gradient computation, accelerating the minimization of the objective functions.

Fast and Robust Reconstruction for Fluorescence Molecular Tomography via L1-2 Regularization

Sparse reconstruction inspired by compressed sensing has attracted considerable attention in fluorescence molecular tomography (FMT). However, the columns of system matrix used for FMT reconstruction tend to be highly coherent, which means L₁ minimization may not produce the sparsest solution. In this paper, we propose a novel reconstruction method by minimization of the difference of L₁ and L₂ norms. To solve the nonconvex L_1-2 minimization problem, an iterative method based on the difference of convex algorithm (DCA) is presented. In each DCA iteration, the update of solution involves an L₁ minimization subproblem, which is solved by the alternating direction method of multipliers with an adaptive penalty. We investigated the performance of the proposed method with both simulated data and in vivo experimental data. The results demonstrate that the DCA for L_1-2 minimization outperforms the representative algorithms for L₁, L₂, L_1/2, and L₀ when the system matrix is highly coherent.

Local motion-compensated method for high-quality 3D coronary artery reconstruction

The 3D reconstruction of coronary artery from X-ray angiograms rotationally acquired on C-arm has great clinical value. While cardiac-gated reconstruction has shown promising results, it suffers from the problem of residual motion. This work proposed a new local motion-compensated reconstruction method to handle this issue. An initial image was firstly reconstructed using a regularized iterative reconstruction method. Then a 3D/2D registration method was proposed to estimate the residual vessel motion. Finally, the residual motion was compensated in the final reconstruction using the extended iterative reconstruction method. Through quantitative evaluation, it was found that high-quality 3D reconstruction could be obtained and the result was comparable to state-of-the-art method.