ADMM based low-rank and sparse matrix recovery method for sparse photoacoustic microscopy

Abstract Photoacoustic microscopy (PAM) has evolved into a new promising medical imaging tool available for both in vivo surficial and deep-tissue imaging with a high spatial resolution. However, the long data acquisition time has made real-time imaging highly challenging. This paper presents an Alternating Direction Method of Multipliers (ADMM) based low-rank and sparse matrix recovery method for a sparse optical-scanning PAM system to realize fast PAM vascular imaging. For our system, an x-y galvanometer scanner is used to achieve compressive sampling, and the associated image recovery process is formulated as a matrix completion problem. The sparse scanning scheme might be easy to integrate with several other optical-resolution PAM modalities. Further, the sparse constraint (the total variation norm) and the low-rank constraint (nuclear norm) are combined for solving the optimization program under ADMM framework for matrix recovery in order to achieve better PAM image recovery even for images that are not well-approximated by their low-rank components. A prototype PAM system has been implemented and the recovery method has been validated. From both visual effects and quantitative parameters, such as PSNR, SSIM, Rerr and MSE, comparable image qualities with conventional full sampling optical resolution PAM could be acquired by just half of the data acquisition time. Besides, the ADMM based low-rank and sparse matrix recovery method could show better results than GoDec. The obtained results demonstrate the preclinical and clinical potential of sparse PAM system in investigating vascular diseases.