Sparse Reconstruction based on K-Sparse Dictionary Learning Method for Bioluminescence Tomography

Bioluminescence tomography (BLT) is an important branch of molecular imaging, holds great prospect in biomedical research. However, BLT reconstruction results are often sensitive and inaccurate due to its inherently ill-posed property of inverse problem. Conventional BLT reconstruction methods based on dictionary learning suffer from slow convergence speed and prone to trap in sub-optimal solutions. To address these problems, this paper proposes an accelerated forward-backward splitting and the difference of convex functions algorithm (AFBS-DCA) based on dictionary learning framework. In the sparse coding stage, the non-convex Generalized Minimax-Concave (GMC) regularization is utilized to improve the sparsity of the sparse coefficient vector, the Nesterov's acceleration technique is integrated in AFBS algorithm to improve the global convergence performance and the k-sparsity strategy is innovatively introduced to achieve adaptive adjustment of the regularization parameter. In the dictionary updating stage, DCA is used to reduce the complexity of the objective function by decomposing the problem into easy and solvable sub-problems. Numerical simulation experiments verified the performance of the proposed method by comparing with two traditional reconstruction methods respectively. The results demonstrate that AFBS-DCA method has superior performance in terms of localization accuracy and shape recovery ability.Clinical Relevance- The AFBS-DCA method proposed in this paper enhances BLT reconstruction efficiency and accuracy, providing new opportunities to deepen insights into disease mechanisms and assess drug efficacy in preclinical and clinical studies.