Reconstruction algorithm for photoacoustic tomography based on the L-alternating direction method of multipliers model.

Significance: Photoacoustic tomography (PAT) is an emerging biomedical imaging technology that offers high contrast and high resolution, showing great potential for applications in medical imaging. However, existing regularization methods often lead to instability and artifacts in the reconstruction due to imbalanced regularization parameter settings. To address these issues, we propose a reconstruction algorithm based on the L-alternating direction method of multipliers (ADMM) for PAT, which significantly improves image reconstruction quality and has high clinical application potential. Aim: We introduce a nonconvex L1-L2 norm into the variational model and employ the ADMM to decompose the optimization problem into efficiently solvable subproblems. A preconditioned conjugate gradient (PCG) method is further integrated to accelerate the solution of linear systems, thereby improving both reconstruction accuracy and computational efficiency. Approach: We propose an L-ADMM framework with adaptive weighted L1-L2 regularization for PAT reconstruction. The method employs ADMM to split the optimization into tractable subproblems and uses PCG to efficiently solve linear systems. It achieves stable, high-quality reconstruction under sparse sampling by enhancing sparsity while preserving structural details. Results: Experiments on vascular and breast models demonstrate that, even with only 64 transducers under sparse sampling, the proposed L-ADMM method achieves peak signal-to-noise ratio values of 37.24 and 36.26 dB and structural similarity index measure values of 0.9766 and 0.9665, respectively. Compared with L2, L1 + L2, L1-L2, TV regularization, and U-Net methods, the proposed algorithm substantially improves image quality, highlighting its feasibility for cost-effective clinical PAT. Conclusions: The proposed L-ADMM-based reconstruction algorithm, by integrating adaptive regularization with efficient optimization, significantly improves PAT image quality under sparse sampling conditions, offering a feasible solution with strong potential for clinical translation.