Fluorescence Molecular Tomography Reconstruction Research Articles

Augmented flexible Krylov subspace methods with applications to Bayesian inverse problems

This paper presents two new augmented flexible (AF)-Krylov subspace methods, AF-GMRES and AF-LSQR, to compute solutions of large-scale linear discrete ill-posed problems that can be modeled as the sum of two independent random variables, exhibiting smooth and sparse stochastic characteristics respectively. Following a Bayesian modeling approach, this corresponds to adding a covariance-weighted quadratic term and a sparsity enforcing ℓ1 term in the original least-squares minimization scheme. To handle the ℓ1 regularization term, the proposed approach constructs a sequence approximating quadratic problems that are partially solved using augmented flexible Krylov–Tikhonov methods.Compared to other traditional methods used to solve this minimization problem, such as those based on iteratively reweighted norm schemes, the new algorithms build a single (augmented, flexible) approximation (Krylov) subspace that encodes information about the different regularization terms through adaptable “preconditioning”. The solution space is then expanded as soon as a new problem within the sequence is defined. This also allows for the regularization parameters to be chosen on-the-fly at each iteration. Compared to most recent work on generalized flexible Krylov methods [6], our methods offer theoretical assurance of convergence and a more stable numerical performance. The efficiency of the new methods is shown through a variety of experiments, including a synthetic image deblurring problem, a synthetic atmospheric transport problem, and fluorescence molecular tomography reconstructions using both synthetic and real-world experimental data.

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.

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

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

Adaptive Sparsity Orthogonal Least Square with Neighbor Strategy for Fluorescence Molecular Tomography.

Fluorescence molecular tomography (FMT) is a highly sensitive and noninvasive optical imaging technique which has been widely applied to disease diagnosis and drug discovery. However, FMT reconstruction is a highly ill-posed problem. In this work, L0-norm regularization is employed to construct the mathematical model of the inverse problem of FMT. And an adaptive sparsity orthogonal least square with a neighbor strategy (ASOLS-NS) is proposed to solve this model. This algorithm can provide an adaptive sparsity and can establish the candidate sets by a novel neighbor expansion strategy for the orthogonal least square (OLS) algorithm. Numerical simulation experiments have shown that the ASOLS-NS improves the reconstruction of images, especially for the double targets reconstruction.Clinical relevance- The purpose of this work is to improve the reconstruction results of FMT. Current experiments are focused on simulation experiments, and the proposed algorithm will be applied to the clinical tumor detection in the future.

Neighbor-based adaptive sparsity orthogonal least square for fluorescence molecular tomography.

Fluorescence molecular tomography (FMT) is a promising imaging modality, which has played a key role in disease progression and treatment response. However, the quality of FMT reconstruction is limited by the strong scattering and inadequate surface measurements, which makes it a highly ill-posed problem. Improving the quality of FMT reconstruction is crucial to meet the actual clinical application requirements. We propose an algorithm, neighbor-based adaptive sparsity orthogonal least square (NASOLS), to improve the quality of FMT reconstruction. The proposed NASOLS does not require sparsity prior information and is designed to efficiently establish a support set using a neighbor expansion strategy based on the orthogonal least squares algorithm. The performance of the algorithm was tested through numerical simulations, physical phantom experiments, and small animal experiments. The results of the experiments demonstrated that the NASOLS significantly improves the reconstruction of images according to indicators, especially for double-target reconstruction. NASOLS can recover the fluorescence target with a good location error according to simulation experiments, phantom experiments and small mice experiments. This method is suitable for sparsity target reconstruction, and it would be applied to early detection of tumors.

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

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

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

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

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

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

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

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

Robust reconstruction of fluorescence molecular tomography based on adaptive adversarial learning strategy

Objective. Fluorescence molecular tomography (FMT) is a promising molecular imaging modality for quantifying the three-dimensional (3D) distribution of tumor probes in small animals. However, traditional deep learning reconstruction methods that aim to minimize the mean squared error (MSE) and iterative regularization algorithms that rely on optimal parameters are typically influenced by strong noise, resulting in poor FMT reconstruction robustness. Approach. In this letter, we propose an adaptive adversarial learning strategy (3D-UR-WGAN) to achieve robust FMT reconstructions. Unlike the pixel-based MSE criterion in traditional CNNs or the regularization strategy in iterative solving schemes, the reconstruction strategy can greatly facilitate the performance of the network models through alternating loop training of the generator and the discriminator. Second, the reconstruction strategy combines the adversarial loss in GANs with the L1 loss to significantly enhance the robustness and preserve image details and textual information. Main results. Both numerical simulations and physical phantom experiments demonstrate that the 3D-UR-WGAN method can adaptively eliminate the effects of different noise levels on the reconstruction results, resulting in robust reconstructed images with reduced artifacts and enhanced image contrast. Compared with the state-of-the-art methods, the proposed method achieves better reconstruction performance in terms of target shape recovery and localization accuracy. Significance. This adaptive adversarial learning reconstruction strategy can provide a possible paradigm for robust reconstruction in complex environments, and also has great potential to provide an alternative solution for solving the problem of poor robustness encountered in other optical imaging modalities such as diffuse optical tomography, bioluminescence imaging, and Cherenkov luminescence imaging.

High-Resolution Reconstruction of FMT Based on Elastic Net Optimized by Relaxed ADMM.

Fluorescence Molecular Tomography (FMT), providing thethree-dimensional fluorescent distribution information of specific molecular probes in tumors, is widely applied to detect in vivo tumors. However, the ill-posedness of reconstruction greatly affects the resolution of FMT. Traditional methods have introduced different regularization terms to solve this problem, but there are still challenges for the high-resolution reconstruction of small tumors under complex conditions. In this paper, we proposed an elastic net method optimized by the relaxed Alternating Direction Method of Multipliers (EN-RADMM) to improve the reconstruction resolution for small tumors. The objective function consisted of the Least-Square term and elastic net regularization. Relaxation, equivalent deformation directing at ill-posed equations, and LU decomposition were applied to accelerate algorithm convergence and improve solution accuracy. Thereby, the light from small tumors can be precisely reconstructed. We designed a series of digital tumor models with different distances, sizes, and shapes to verify the performance of EN-RADMM, and utilized the real glioma-bearing mouse models to further verify its feasibility and accuracy. The simulation results demonstrated that EN-RADMM can achieve significantly higher resolution and reconstruction accuracy of morphology and position with less time compared with other advanced methods. Furthermore, in vivo experiments proved the broad prospect of EN-RADMM in pre-clinical application of FMT reconstruction.

Excitation-based fully connected network for precise NIR-II fluorescence molecular tomography.

Fluorescence molecular tomography (FMT) is a novel imaging modality to obtain fluorescence biomarkers' three-dimensional (3D) distribution. However, the simplified mathematical model and complicated inverse problem limit it to achieving precise results. In this study, the second near-infrared (NIR-II) fluorescence imaging was adopted to mitigate tissue scattering and reduce noise interference. An excitation-based fully connected network was proposed to model the inverse process of NIR-II photon propagation and directly obtain the 3D distribution of the light source. An excitation block was embedded in the network allowing it to autonomously pay more attention to neurons related to the light source. The barycenter error was added to the loss function to improve the localization accuracy of the light source. Both numerical simulation and in vivo experiments showed the superiority of the novel NIR-II FMT reconstruction strategy over the baseline methods. This strategy was expected to facilitate the application of machine learning in biomedical research.

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.

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

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

An extraction strategy to determine a permissible region for fluorescence molecular tomography

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.

UHR-DeepFMT: Ultra-High Spatial Resolution Reconstruction of Fluorescence Molecular Tomography Based on 3-D Fusion Dual-Sampling Deep Neural Network.

Fluorescence molecular tomography (FMT) is a promising and high sensitivity imaging modality that can reconstruct the three-dimensional (3D) distribution of interior fluorescent sources. However, the spatial resolution of FMT has encountered an insurmountable bottleneck and cannot be substantially improved, due to the simplified forward model and the severely ill-posed inverse problem. In this work, a 3D fusion dual-sampling convolutional neural network, namely UHR-DeepFMT, was proposed to achieve ultra-high spatial resolution reconstruction of FMT. Under this framework, the UHR-DeepFMT does not need to explicitly solve the FMT forward and inverse problems. Instead, it directly establishes an end-to-end mapping model to reconstruct the fluorescent sources, which can enormously eliminate the modeling errors. Besides, a novel fusion mechanism that integrates the dual-sampling strategy and the squeeze-and-excitation (SE) module is introduced into the skip connection of UHR-DeepFMT, which can significantly improve the spatial resolution by greatly alleviating the ill-posedness of the inverse problem. To evaluate the performance of UHR-DeepFMT network model, numerical simulations, physical phantom and in vivo experiments were conducted. The results demonstrated that the proposed UHR-DeepFMT can outperform the cutting-edge methods and achieve ultra-high spatial resolution reconstruction of FMT with the powerful ability to distinguish adjacent targets with a minimal edge-to-edge distance (EED) of 0.5 mm. It is assumed that this research is a significant improvement for FMT in terms of spatial resolution and overall imaging quality, which could promote the precise diagnosis and preclinical application of small animals in the future.

A Novel Adaptive Parameter Search Elastic Net Method for Fluorescent Molecular Tomography

Fluorescence molecular tomography (FMT) is a new type of medical imaging technology that can quantitatively reconstruct the three-dimensional distribution of fluorescent probes in vivo. Traditional Lp norm regularization techniques used in FMT reconstruction often face problems such as over-sparseness, over-smoothness, spatial discontinuity, and poor robustness. To address these problems, this paper proposes an adaptive parameter search elastic net (APSEN) method that is based on elastic net regularization, using weight parameters to combine the L1 and L2 norms. For the selection of elastic net weight parameters, this approach introduces the L0 norm of valid reconstruction results and the L2 norm of the residual vector, which are used to adjust the weight parameters adaptively. To verify the proposed method, a series of numerical simulation experiments were performed using digital mice with tumors as experimental subjects, and in vivo experiments of liver tumors were also conducted. The results showed that, compared with the state-of-the-art methods with different light source sizes or distances, Gaussian noise of 5%-25%, and the brute-force parameter search method, the APSEN method has better location accuracy, spatial resolution, fluorescence yield recovery ability, morphological characteristics, and robustness. Furthermore, the in vivo experiments demonstrated the applicability of APSEN for FMT.

A Multimodality Image Guided Precision Radiation Research Platform: Integrating X-ray, Bioluminescence, and Fluorescence Tomography With Radiation Therapy

Small animal irradiation is crucial to the investigation of radiobiological mechanisms. The paradigm of clinical radiation therapy is trending toward high-precision, stereotactic treatment. However, translating this scheme to small animal irradiation is challenging owing to the lack of high-quality image guidance. To overcome this obstacle, we developed a multimodality image guided precision radiation platform. The platform consists of 4 modules: x-ray computed tomography (CT), bioluminescence tomography (BLT), fluorescence molecular tomography (FMT), and radiation therapy. CT provides animal anatomy and material density for radiation dose calculation, as well as body contour for BLT and FMT reconstruction. BLT and FMT provide tumor localization to guide radiation beams and molecular activity to evaluate treatment outcome. Furthermore, we developed a Monte Carlo-based treatment planning system (TPS) for 3-dimensional dose calculation, calibrated it using radiochromic films sandwiched in a water-equivalent phantom, and validated it using invivo dosimeters surgically implanted into euthanized mice (n = 4). Finally, we performed image guided irradiation on mice bearing orthotopic breast and prostate tumors and confirmed radiation delivery using γH2AX histology. The Monte Carlo-based TPS was successfully calibrated by benchmarking simulation dose against film measurement. For invivo dosimetry measured in the euthanized mice, the average difference between the TPS calculated dose and measured dose was 3.86% ± 1.12%. Following the TPS-generated treatment plan, we successfully delivered 20 Gy dose to an animal bearing an orthotopic prostate tumor using 4 BLT-guided radiation beams and 5 Gy dose to an animal bearing an orthotopic breast tumor using a single FMT-guided radiation beam. γH2AX histology presented significantly more DNA damage in irradiated tumors and thus validated the dose delivery accuracy. Combined with Monte Carlo TPS, this multimodality CT/BLT/FMT image guided small animal radiation platformcan specifically localize tumors, accurately calculate dose distribution, precisely guide radiation delivery, and molecularly evaluate treatment response. It provides an advanced toolset for radiobiology and translational cancer research.

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

Fluorescence molecular tomography (FMT) is a highly sensitive and noninvasive imaging modality for three-dimensional visualization of fluorescence probe distribution in small animals. However, the simplified photon propagation model and ill-posed inverse problem limit the improvement of FMT reconstruction. In this work, we proposed a novel K-nearest neighbor based locally connected (KNN-LC) network to improve the performance of morphological reconstruction in FMT. It directly builds the inverse process of photon transmission by learning the mapping relation between the surface photon intensity and the distribution of fluorescent source. KNN-LC network cascades a fully connected (FC) sub-network with a locally connected (LC) sub-network, where the FC part provides a coarse reconstruction result and LC part fine-tunes the morphological quality of reconstructed result. To assess the performance of our proposed network, we implemented both numerical simulation and in vivo studies. Furthermore, split Bregman-resolved total variation (SBRTV) regularization method and inverse problem simulation (IPS) method were utilized as baselines in all comparisons. The results demonstrated that KNN-LC network achieved accurate reconstruction in both source localization and morphology recovery in a short time. This promoted the in vivo application of FMT for visualizing the distribution of biomarkers inside biological tissue.