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

•This article proposed the ADMM based low-rank and sparse matrix recovery method for sparse photoacoustic microscopy to achieve fast imaging.•Compressive sampling is achieved by an x-y galvanometer scanner, and the image recovery process is formulated as a matrix completion problem.•The sparse constraint (total variation norm) and the low-rank constraint (nuclear norm) are combined for solving the image recovery problem.•The sparse and low-rank matrix completion problem is solved under ADMM to achieve better PAM image.•A prototype PAM system has been implemented and the recovery method has been validated with both visual effects and quantitative parameters.