Poisson image restoration with likelihood constraint via hybrid steepest descent method

This paper proposes a likelihood constrained optimization framework for Poisson image restoration. The likelihood constrained problem considered in this paper is the minimization of convex priors over the level set of the negative-log-likelihood function of the Poisson distribution. It has advantages in parameter selection compared with the minimization of the weighted sum of convex priors and the negative-log-likelihood function, which has been used in conventional methods. The level set is characterized as the fixed point set of a certain quasi-nonexpansive operator, which enables us to apply the hybrid steepest descent method to solve the constrained problem. The proposed framework not only can handle the level set of any convex function whose subgradient is available but also does not require any computationally-expensive procedure such as operator inversion and inner loop. Illustrative numerical examples are also presented.