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Background and Objective: Bioluminescence tomography (BLT) is a noninvasive optical imaging technique that provides qualitative and quantitative information on the spatial distribution of tumors in living animals. Researchers have proposed a list of algorithms and strategies for BLT reconstruction to improve its reconstruction quality. However, multi-target BLT reconstruction remains challenging in practical clinical applications due to the mutual interference of optical signals and difficulty in source separation., Methods: To solve this problem, this study proposes the subspace decision optimization (SDO) approach based on the traditional iterative permissible region strategy. The SDO approach transforms a single permissible region into multiple subspaces by clustering analysis. These subspaces are shrunk based on subspace shrinking optimization to achieve spatial continuity of the permissible regions. In addition, these subspaces are merged to construct a new permissible region and then the next iteration of reconstruction is carried out to ensure the stability of the results. Finally, all the iterative results are optimized based on the normal distribution model and the distribution properties of the targets to ensure the sparsity of each target and the non-biasing of the overall results., Results: Experimental results show that the SDO approach can automatically identify and separate different targets, ensuring the accuracy and quality of multi-target BLT reconstruction results. Meanwhile, SDO can combine various types of reconstruction algorithms and provide stable and high-quality reconstruction results independent of the algorithm parameters., Conclusions: The SDO approach provides an integrated solution to the multi-target BLT reconstruction problem, realizing the whole process including target recognition, separation, reconstruction, and result enhancement, which can extend the application domain of BLT., Competing Interests: Declaration of Competing Interest The authors declare that no conflict of interest., (Copyright © 2023 Elsevier B.V. All rights reserved.)

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.

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 l 2 -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 l 1 (TL1) metric that interpolates l 0 and l 1 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., Competing Interests: Declaration of Competing Interest The authors declare that they have no competing financial interests or personal relationships that may have influenced the work reported in this study., (Copyright © 2023 Elsevier B.V. All rights reserved.)

Background and Objective: Bioluminescence tomography (BLT) is a powerful and sensitive imaging technique having great potential in preclinical application, such as tumor imaging, monitoring and therapy, etc. Regularization plays an important role in BLT reconstruction for considering the priori information to overcome the inherent ill-posedness of the inverse problem. Therefore, well-designed regularization term and sophisticated algorithm for solving the consequent optimization problem are key to improve the BLT quality., Methods: To balance the sparsity, smoothness and morphological characteristics of the bioluminescence targets, we constructed a novel Graph-Guided Hybrid Regularization (GGHR) method by combining graph-guided penalty term with L 1 and L 2 norm regularizer. To solve the corresponding minimization problem with hybrid penalties, the dual decomposition and Nesterov's smoothing technique were adopted to decouple and transform the non-separable and non-smooth graph-guided penalty term into a differential smooth approximation form, which was solved by the fast iterative shrinkage thresholding algorithm., Results: The performance of the proposed GGHR method was verified and evaluated through a series of simulation, phantom and in vivo experiments. The comparison results demonstrated that the GGHR method outperformed current mainstream reconstruction algorithms in spatial localization, morphology recovery and in vivo practicality., Conclusions: The proposed GGHR method is a robust and practicality reconstruction algorithm for further highlighting the positive effect of hybrid regularization on BLT applications., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2022 Elsevier B.V. All rights reserved.)

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.

Bioluminescence tomography (BLT) has important applications in the in vivo visualization of a pathological process for preclinical studies. However, the reconstruction of BLT is severely ill-posed. To recover the bioluminescence source stably and efficiently, we use a log-sum regularization term in the objective function and utilize a hybrid optimization algorithm for solving the nonconvex regularized problems (HONOR). The hybrid optimization scheme of HONOR merges second-order information and first-order information to reconstruction by choosing either the quasi-Newton (QN) or gradient descent step at each iteration. The QN step uses the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm (L-BFGS) to acquire second-order information. Simulations and in vivo experiments based on multispectral measurements demonstrated the remarkable performance of the proposed hybrid method in the sparse reconstruction of BLT.

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., (© 2020 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

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.

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., (© 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

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.

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.

Fluorescence molecular tomography (FMT) is a promising imaging modality that offers the possibilities to monitor cellular and molecular function in vivo. However, accurate and stable reconstruction of fluorescence-labeled targets remains a challenging problem. In this contribution, a two-stage reconstruction algorithm that combines sparse regularization with adaptive finite element method is proposed, and two different inversion algorithms are employed separately on the initial coarse mesh and the second refined one. Numerical experiment results with a digital mouse model demonstrate the stability and computational efficiency of the proposed method for FMT.

Bioluminescence tomography (BLT) is an inherent ill-posed inverse problem to reconstruct the internal source in 3-D with limited measurements on the external surface. In most BLT studies so far, a relatively small permissible source region or multispectral approach is typically used to enhance the stability or quality of the solution. In this letter, considering the sparsity characteristic of the light source, BLT is reformulated as a least absolute shrinkage and selection operator (LASSO) problem with l(1) regularization, and then, a fast reconstruction algorithm named as stagewise fast LASSO is proposed for solving this problem. Numerical simulations of a 3-D mouse atlas under different noise levels demonstrate that the proposed algorithm is robust against measurement noise, and it can achieve high computational efficiency and accurate localization of source even without any permissible region constraint.

Objective. Pharmacokinetic parametric images obtained through dynamic fluorescence molecular tomography (DFMT) has ability of capturing dynamic changes in fluorescence concentration, thereby providing three-dimensional metabolic information for applications in biological research and drug development. However, data processing of DFMT is time-consuming, involves a vast amount of data, and the problem itself is ill-posed, which significantly limits the application of pharmacokinetic parametric images reconstruction. In this study, group sparse-based Taylor expansion method is proposed to address these problems. Approach. Firstly, Taylor expansion framework is introduced to reduce time and computational cost. Secondly, group sparsity based on structural prior is introduced to improve reconstruction accuracy. Thirdly, alternating iterative solution based on accelerated gradient descent algorithm is introduced to solve the problem. Main results. Numerical simulation and in vivo experimental results demonstrate that, in comparison to existing methods, the proposed approach significantly enhances reconstruction speed without a degradation of quality, particularly when confronted with background fluorescence interference from other organs. Significance. Our research greatly reduces time and computational cost, providing strong support for real-time monitoring of liver metabolism. [ABSTRACT FROM AUTHOR]

Fluorescence molecular tomography (FMT) is an optical molecular tomography technology with great promise, and it has broad application prospects for its high sensitivity. However, it is still a challenge in reconstruction because of its severe ill-posedness. In this study, a new extraction strategy to determine a permissible region of target is proposed for FMT, which can provide a definite central position and size of the permissible region. Numerical simulation experiments and an in vivo experiment have been carried out to verify the performances of the strategy. The experimental results demonstrated that the strategy can provide a permissible region of target with a definite position and size, which further allowed a steady and accurate reconstruction for FMT. [ABSTRACT FROM AUTHOR]

Bioluminescence tomography (BLT) is a promising in vivo molecular imaging tool that allows non-invasive monitoring of physiological and pathological processes at the cellular and molecular levels. However, the accuracy of the BLT reconstruction is significantly affected by the forward modeling errors in the simplified photon propagation model, the measurement noise in data acquisition, and the inherent ill-posedness of the inverse problem. In this paper, we present a new multispectral differential strategy (MDS) on the basis of analyzing the errors generated from the simplification from radiative transfer equation (RTE) to diffusion approximation and data acquisition of the imaging system. Through rigorous theoretical analysis, we learn that spectral differential not only can eliminate the errors caused by the approximation of RTE and imaging system measurement noise but also can further increase the constraint condition and decrease the condition number of system matrix for reconstruction compared with traditional multispectral (TM) reconstruction strategy. In forward simulations, energy differences and cosine similarity of the measured surface light energy calculated by Monte Carlo (MC) and diffusion equation (DE) showed that MDS can reduce the systematic errors in the process of light transmission. In addition, in inverse simulations and in vivo experiments, the results demonstrated that MDS was able to alleviate the ill-posedness of the inverse problem of BLT. Thus, the MDS method had superior location accuracy, morphology recovery capability, and image contrast capability in the source reconstruction as compared with the TM method and spectral derivative (SD) method. In vivo experiments verified the practicability and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Cerenkov luminescence tomography (CLT) is a promising non-invasive optical imaging method with three-dimensional semiquantitative in vivo imaging capability. However, CLT itself relies on Cerenkov radiation, a low-intensity radiation, making CLT reconstruction more challenging than other imaging modalities. In order to solve the ill-posed inverse problem of CLT imaging, some numerical optimization or regularization methods need to be applied. However, in commonly used methods for solving inverse problems, parameter selection significantly influences the results. Therefore, this paper proposed a probabilistic energy distribution density region scaling (P-EDDRS) framework. In this framework, multiple reconstruction iterations are performed, and the Cerenkov source distribution of each reconstruction is treated as random variables. According to the spatial energy distribution density, the new region of interest (ROI) is solved. The size of the region required for the next operation was determined dynamically by combining the intensity characteristics. In addition, each reconstruction source distribution is given a probability weight value, and the prior probability in the subsequent reconstruction is refreshed. Last, all the reconstruction source distributions are weighted with the corresponding probability weights to get the final Cerenkov source distribution. To evaluate the performance of the P-EDDRS framework in CLT, this article performed numerical simulation, in vivo pseudotumor model mouse experiment, and breast cancer mouse experiment. Experimental results show that this reconstruction framework has better positioning accuracy and shape recovery ability and can optimize the reconstruction effect of multiple algorithms on CLT. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Cerenkov luminescence tomography (CLT) has attracted much attention because of the wide clinically-used probes and three-dimensional (3D) quantification ability. However, due to the serious morbidity of 3D optical imaging, the reconstructed images of CLT are not appreciable, especially when single-view measurements are used. Single-view CLT improves the efficiency of data acquisition. It is much consistent with the actual imaging environment of using commercial imaging system, but bringing the problem that the reconstructed results will be closer to the animal surface on the side where the single-view image is collected. To avoid this problem to the greatest extent possible, we proposed a prior compensation algorithm for CLT reconstruction based on depth calibration strategy. This method takes full account of the fact that the attenuation of light in the tissue will depend heavily on the depth of the light source as well as the distance between the light source and the detection plane. Based on this consideration, a depth calibration matrix was designed to calibrate the attenuation between the surface light flux and the density of the internal light source. The feature of the algorithm was that the depth calibration matrix directly acts on the system matrix of CLT reconstruction, rather than modifying the regularization penalty items. The validity and effectiveness of the proposed algorithm were evaluated with a numerical simulation and a mouse-based experiment, whose results illustrated that it located the radiation sources accurately by using single-view measurements. [ABSTRACT FROM AUTHOR]

Fluorescence molecular tomography (FMT) is a fast-developing optical imaging modality that has great potential in early diagnosis of disease and drugs development. However, reconstruction algorithms have to address a highly ill-posed problem to fulfill 3D reconstruction in FMT. In this contribution, we propose an efficient iterative algorithm to solve the large-scale reconstruction problem, in which the sparsity of fluorescent targets is taken as useful a priori information in designing the reconstruction algorithm. In the implementation, a fast sparse approximation scheme combined with a stage-wise learning strategy enable the algorithm to deal with the ill-posed inverse problem at reduced computational costs. We validate the proposed fast iterative method with numerical simulation on a digital mouse model. Experimental results demonstrate that our method is robust for different finite element meshes and different Poisson noise levels. [ABSTRACT FROM AUTHOR]

Fluorescence molecular tomography (FMT) allows the detection and quantification of various biological processes in small animals in vivo, which expands the horizons of pre-clinical research and drug development. Efficient three-dimensional (3D) reconstruction algorithm is the key to accurate localization and quantification of fluorescent target in FMT. In this paper, 3D reconstruction of FMT is regarded as a sparse signal recovery problem and the compressive sampling matching pursuit (CoSaMP) algorithm is adopted to obtain greedy recovery of fluorescent signals. Moreover, to reduce the modeling error, the simplified spherical harmonics approximation to the radiative transfer equation (RTE), more specifically , is utilized to describe light propagation in biological tissues. The performance of the proposed reconstruction method is thoroughly evaluated by simulations on a 3D digital mouse model by comparing it with three representative greedy methods including orthogonal matching pursuit (OMP), stagewise OMP(StOMP), and regularized OMP (ROMP). The CoSaMP combined with shows an improvement in reconstruction accuracy and exhibits distinct advantages over the comparative algorithms in multiple targets resolving. Stability analysis suggests that CoSaMP is robust to noise and performs stably with reduction of measurements. The feasibility and reconstruction accuracy of the proposed method are further validated by phantom experimental data. [ABSTRACT FROM AUTHOR]

Bioluminescence tomography (BLT) is a promising imaging modality that can provide noninvasive three-dimensional visualization information on tumor distribution. In BLT reconstruction, the widely used methods based on regularization or greedy strategy face problems such as over-sparsity, over-smoothing, spatial discontinuity, poor robustness, and poor multi-target resolution. To deal with these problems, combining the advantages of the greedy strategies as well as regularization methods, we propose a hybrid reconstruction framework for model-based multispectral BLT using the support set of a greedy strategy as a feasible region and the Alpha-divergence to combine the weighted solutions obtained by L 1-norm and L 2-norm regularization methods. In numerical simulations with digital mouse and in vivo experiments, the results show that the proposed framework has better localization accuracy, spatial resolution, and multi-target resolution. [ABSTRACT FROM AUTHOR]

Recently, the simplified spherical harmonics equations (SPN) model has attracted much attention in modeling the light propagation in small tissue geometries at visible and near-infrared wavelengths. In this paper, we report an efficient numerical method for fluorescence molecular tomography (FMT) that combines the advantage of SPN model and adaptive hp finite element method (hp-FEM). For purposes of comparison, hp-FEM and h-FEM are, respectively applied to the reconstruction process with diffusion approximation and SPN model. Simulation experiments on a 3D digital mouse atlas and physical experiments on a phantom are designed to evaluate the reconstruction methods in terms of the location and the reconstructed fluorescent yield. The experimental results demonstrate that hp-FEM with SPN model, yield more accurate results than h-FEM with diffusion approximation model does. The phantom experiments show the potential and feasibility of the proposed approach in FMT applications. [ABSTRACT FROM AUTHOR]