Image reconstruction based on compressed sensing for sparse-data endoscopic photoacoustic tomography.

Endoscopic photoacoustic tomography (EPAT) is an interventional application of photoacoustic tomography (PAT) to visualize anatomical features and functional components of biological cavity structures such as nasal cavity, digestive tract or coronary arterial vessels. One of the main challenges in clinical applicability of EPAT is the incomplete acoustic measurements due to the limited detectors or the limited-view acoustic detection enclosed in the cavity. In this case, conventional image reconstruction methodologies suffer from significantly degraded image quality. This work introduces a compressed-sensing (CS)-based method to reconstruct a high-quality image that represents the initial pressure distribution on a luminal cross-section from incomplete discrete acoustic measurements. The method constructs and trains a complete dictionary for the sparse representation of the photoacoustically-induced acoustic measurements. The sparse representation of the complete acoustic signals is then optimally obtained based on the sparse measurements and a sensing matrix. The complete acoustic signals are recovered from the sparse representation by inverse sparse transformation. The image of the initial pressure distribution is finally reconstructed from the recovered complete signals by using the time reversal (TR) algorithm. It was shown with numerical experiments that high-quality images with reduced under-sampling artifacts can be reconstructed from sparse measurements. The comparison results suggest that the proposed method outperforms the standard TR reconstruction by 40% in terms of the structural similarity of the reconstructed images.