Relaxed ordered subsets algorithm for image restoration of confocal microscopy

The expectation−maximization (EM) algorithm for maximum likelihood image recovery converges very slowly. Thus, the ordered subsets EM (OS−EM) algorithm has been widely used in image reconstruction for tomography due to an order−of−magnitude acceleration over the EM algorithm [1]. However, OS− EM is not guaranteed to converge. The recently proposed ordered subsets, separable paraboloidal surrogates (OS−SPS) algorithm with relaxation has been shown to converge to the optimal point while providing fast convergence [2]. In this paper, we develop a relaxed OS−SPS algorithm for image restoration [3]. Because data acquisition is different in image restoration than in tomography, we adapt a different strategy for choosing subsets in image restoration which uses pixel location rather than projection angles. Simulation results show that the order−of−magnitude acceleration of the relaxed OS−SPS algorithm can be achieved in image restoration.