Investigation of the convergence properties of an iterative image restoration algorithm.

Abstract

Iterative algorithms for image restoration which include the use of prior knowledge of the solution in their design have proven useful in super resolution imaging. In this dissertation, a Bayesian estimation method is presented called the Poisson Maximum A Posteriori (MAP) image restoration algorithm. The Poisson MAP algorithm is shown to be slightly different in its design but similar in super resolution ability to the Poisson Maximum Likelihood (ML) algorithm. Numerical simulations demonstrate that the Poisson MAP algorithm in almost all cases achieves legitimate bandwidth extension and thus achieves super resolution. Practical criteria for indicating when the algorithm has numerically converged are reviewed. The advantages of these criteria are discussed. The theoretical convergence properties of the Poisson MAP algorithm are investigated. The iterative algorithm is viewed as a nonlinear vector mapping in the N-dimensional real Euclidean vector space, Rᴺ. The necessary and sufficient conditions for nonlinear iterative methods of this type to converge are discussed and are shown to be satisfied in certain cases. Although convergence in some cases can only be demonstrated experimentally, convergence can almost always be guaranteed with the right choice of starting vector in cases where super resolution is most needed.