Transformed L1 Regularization for Sparse Photoacoustic Tomography

Photoacoustic Tomography (PAT) is an advanced imaging technology that combines optical and acoustic methods to visualize the distribution of light absorption within biological tissues with high spatial resolution. The reconstruction of PAT images from incomplete and noisy experimental data is an ill-posed problem that requires regularization techniques to ensure meaningful and stable solutions. In this study, a transform L1 (TL1) regularization model was proposed to improve the quality of PAT images, which was evaluated by numerical simulation and tissue phantom experiments. Based on various numerical and tissue phantom scenarios, Gaussian noise levels of 10 to 30 dB, and multiple parameter configurations, the TL1 method consistently demonstrates shows consistent advantages over the Lp-norm ($0 \leq p \leq 2$) regularization methods in terms of image quality, computational efficiency, and noise robustness. This finding has important implications for improving sparse sampling PAT algorithms, and also provides valuable insights for the development of biomedical applications in the future.