Fluorescent molecular tomography (FMT) is a highly sensitive and noninvasive imaging approach for providing three-dimensional distribution of fluorescent marker probes. However, owing to its light scattering effect and the ill-posedness of inverse problems, it is challenging to develop an efficient reconstruction algorithm that can achieve the exact location and morphology of the fluorescence source. In this study, therefore, in order to satisfy the need for early tumor detection and improve the sparsity of solution, we proposed a novel L₁-L₂ norm regularization via the forward-backward splitting method for enhancing the FMT reconstruction accuracy and the robustness. By fully considering the highly coherent nature of the system matrix of FMT, it operates by splitting the objective to be minimized into simpler functions, which are dealt with individually to obtain a sparser solution. An analytic solution of L₁-L₂ norm proximal operators and a forward-backward splitting algorithm were employed to efficiently solve the nonconvex L₁-L₂ norm minimization problem. Numerical simulations and an in-vivo glioma mouse model experiment were conducted to evaluate the performance of our algorithm. The comparative results of these experiments demonstrated that the proposed algorithm obtained superior reconstruction performance in terms of spatial location, dual-source resolution, and in-vivo practicability. It was believed that this study would promote the preclinical and clinical applications of FMT in early tumor detection.

Objective: Fluorescence Molecular Tomography (FMT) is a promising optical tool for small animal imaging. The $\ell_{1/2}$ -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 non-convex 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 non-convex optimization model. Specifically, the half thresholding iteration method is utilized to solve $\ell_{1/2}$ -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 (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.

As a high-sensitivity and non-invasive technique, optical molecular tomography (OMT) can locate and visualize tissue quantitatively in three dimensions by collecting surface photons generated from luminescent biomarkers. It has great potential for tumor detection, surgery guidance, and pharmacokinetics research studies. However, due to the limited measurable surface photons and the highly scattered feature of photons, the reconstruction of OMT is highly ill-posed and ill-conditioned, which limits the performance in practice. To improve the accuracy of OMT, plenty of studies focus on precisely modeling photon propagation and accurately reconstructing light source. Since these methods are carried out based on different theories, we review famous solutions for the reconstruction in terms of the photon propagation models and inverse reconstruction algorithms to make an overall understanding for the methods of OMT reconstruction. Additionally, some prospects are listed to provide possible research orientation that may benefit future research.

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.