A multi-grid method for joint reconstruction of initial pressure and speed of sound in photoacoustic tomography

Based on the photoacoustic effect, photoacoustic tomography (PAT) illuminates biological tissue with modulated light to obtain high-contrast images non-invasively, making it increasingly popular in biomedical and life sciences. In practical applications, the varying speed of sound (SOS) in biological tissue is a critical factor influencing the quality of reconstructed images. Among various reconstruction methods addressing this heterogeneity, joint reconstruction (JR) has emerged as a promising approach since it can recover both the initial pressure (IP) and SOS simultaneously, based solely on detected signals, without requiring prior knowledge of the SOS or additional ultrasound equipment. However, traditional JR suffers from two key limitations: 1) the SOS inversion problem is ill-posed, and 2) the alternating iterative solution for IP and SOS incurs very high computational costs. In this study, we introduce a multi-grid iterative strategy into the JR framework, addressing the inverse problem across multi-scale grids and coupling the results from different scales of grids. Specifically, computation begins on the coarse grids, with the reconstruction results serving as high-quality initial estimates for subsequent iterations on the fine grids. This process ultimately reconstructs the distributions of IP and SOS on the target grid successfully. Through numerical simulations, the proposed method is compared with traditional methods in terms of imaging quality and speed. The results demonstrate that the multi-grid iterative strategy significantly accelerates the speed of JR while preserving accuracy. The proposed multi-grid JR method is highly cost-effective in providing high-quality reconstructions and has the potential to offer valuable guidance for the practical applications of JR.