Adaptive k-sparse constrained dictionary learning strategy for bioluminescence tomography reconstruction.

Objective: Bioluminescence tomography (BLT) is a significant molecular imaging modality with promising potential in biomedical research. However, the reconstruction results of BLT are frequently sensitive and imprecise due to the light scattering effect and ill-posed inverse problem.

Approach: We propose an accelerated forward-backward splitting and the difference of convex functions algorithm (AFBS-DCA) based on a dictionary learning framework. In the sparse coding phase, a k-sparsity strategy enables adaptive adjustment of the regularization parameter, improving the overall efficiency. The non-convex generalized minimax-concave (GMC) regularization is employed to enhance sparsity, while Nesterov's acceleration strategy improves convergence speed. During dictionary updating, DCA is utilized to efficiently solve a non-convex optimization problem modelled as a difference of two convex functions, effectively reducing computational complexity.

Main results: The effectiveness of the AFBS-DCA method was evaluated through numerical simulations and light source implantation experiments. It achieved the highest reconstruction accuracy with an average localization error (LE) of 0.391 mm, an average Dice coefficient (DICE) of 0.774, and a contrast-to-noise ratio (CNR) of 0.872. Compared with three baseline methods, the AFBS-DCA reduced reconstruction errors by 62.8%, 52.5%, and 37.8%, respectively.

Significance: The proposed AFBS-DCA method demonstrates superior performance in terms of localization accuracy, morphological recovery, and robustness, indicating its potential to advance the practical application of BLT in biomedical research and molecular imaging.