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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., (© 2024 Institute of Physics and Engineering in Medicine.)

Dynamic fluorescence molecular tomography (DFMT), as a noninvasive optical imaging method, can quantify metabolic parameters of living animal organs and assist in the diagnosis of metabolic diseases. However, existing DFMT methods do not have a high capacity to reconstruct abnormal metabolic regions, and require additional prior information and complicated solution methods. This paper introduces a problem decomposition and prior refactor (PDPR) method. The PDPR decomposes the metabolic parameters into two kinds of problems depending on their temporal coupling, which are solved using regularization and parameter fitting. Moreover, PDPR introduces the idea of divide-and-conquer to refactor prior information to ensure discrimination between metabolic abnormal regions and normal tissues. Experimental results show that PDPR is capable of separating abnormal metabolic regions of the liver and has the potential to quantify metabolic parameters and diagnose liver metabolic diseases in small animals., (© 2024 Wiley‐VCH GmbH.)

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.)

Harnessing the power and flexibility of radiolabeled molecules, Cerenkov luminescence tomography (CLT) provides a novel technique for non-invasive visualisation and quantification of viable tumour cells in a living organism. However, owing to the photon scattering effect and the ill-posed inverse problem, CLT still suffers from insufficient spatial resolution and shape recovery in various preclinical applications. In this study, we proposed a total variation constrained graph manifold learning (TV-GML) strategy for achieving accurate spatial location, dual-source resolution, and tumour morphology. TV-GML integrates the isotropic total variation term and dynamic graph Laplacian constraint to make a trade-off between edge preservation and piecewise smooth region reconstruction. Meanwhile, the tetrahedral mesh-Cartesian grid pair method based on the k-nearest neighbour, and the adaptive and composite Barzilai-Borwein method, were proposed to ensure global super linear convergence of the solution of TV-GML. The comparison results of both simulation experiments and in vivo experiments further indicated that TV-GML achieved superior reconstruction performance in terms of location accuracy, dual-source resolution, shape recovery capability, robustness, and in vivo practicability. Significance: We believe that this novel method will be beneficial to the application of CLT for quantitative analysis and morphological observation of various preclinical applications and facilitate the development of the theory of solving inverse problem.

X-ray luminescence computed tomography (XLCT) uses external X-rays for luminescence excitation, which is becoming a promising molecular imaging technique with superb penetration depth and spatial resolution. To achieve the tomographic mapping of luminescence distribution, accurate optical propagation model and suitable reconstruction method are two keys for XLCT, but not satisfied. To overcome the limitation of the single proton propagation model (e.g., DE, SP 3 ), we adopted a hybrid diffusion equation with third order simplified spherical harmonics (DE-SP 3 ) model for XLCT. To enable fast iteration and accurate sparse reconstruction, we also integrated in the inversion optimization, with a novel Least Square QR-factorization based on the Lasso (Lasso-LSQR) algorithm. We first simulated the light propagation in various kinds of organs under DE model and SP 3 model, respectively. By comparison with the Monte Carlo, these tissues can be categorized into two types, namely DE-fitted tissues that include muscle and lung, and SP 3 -fitted tissues including heart, kidney, liver, and stomach. According to the above classification results, we built a hybrid DE-SP 3 model to more accurately describing light transport. Numerical simulations and in vivo experiments illustrated that hybrid DE-SP 3 model achieves superior reconstruction performance in terms of location accuracy, and spatial resolution than DE, and less computational cost than SP 3 . The hybrid DE-SP 3 model materializes a balance between accuracy and efficiency for XLCT., (© 2021 Wiley-VCH GmbH.)

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-ℓ 1 ℓ 2 reconstruction method is proposed aiming to the challenge. Approach . Firstly, our approach consists of ℓ 1 and ℓ 2 regularization 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-ℓ 1 ℓ 2 regulazation. 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-ℓ 1 ℓ 2 method, numerical simulations, phantom and in vivo experiments were conducted. In these experiments, the Elastic net-ℓ 1 ℓ 2 method 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-ℓ 1 ℓ 2 can 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., (© 2021 Institute of Physics and Engineering in Medicine.)

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.

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.

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.

Quantitative reconstruction of bioluminescent sources from boundary measurements is a challenging ill-posed inverse problem owing to the high degree of absorption and scattering of light through tissue. We present a hybrid multilevel reconstruction scheme by combining the ability of sparse regularization with the advantage of adaptive finite element method. In view of the characteristics of different discretization levels, two different inversion algorithms are employed on the initial coarse mesh and the succeeding ones to strike a balance between stability and efficiency. Numerical experiment results with a digital mouse model demonstrate that the proposed scheme can accurately localize and quantify source distribution while maintaining reconstruction stability and computational economy. The effectiveness of this hybrid reconstruction scheme is further confirmed with in vivo experiments.

In this paper, we present an incomplete variables truncated conjugate gradient (IVTCG) method for bioluminescence tomography (BLT). Considering the sparse characteristic of the light source and insufficient surface measurement in the BLT scenarios, we combine a sparseness-inducing (ℓ1 norm) regularization term with a quadratic error term in the IVTCG-based framework for solving the inverse problem. By limiting the number of variables updated at each iterative and combining a variable splitting strategy to find the search direction more efficiently, it obtains fast and stable source reconstruction, even without a priori information of the permissible source region and multispectral measurements. Numerical experiments on a mouse atlas validate the effectiveness of the method. In vivo mouse experimental results further indicate its potential for a practical BLT system.

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.