New termination rule for linear iterative image restoration algorithms

Every iterative restoration algorithm requires some performance measure to determine the termination point for the iteration. Typically, the termination rule is based on a measure of the residual or the change in the solution from one iteration to the next. A better rule would be one that terminates the iteration when the distance between the original undistorted image and restored image is minimized in some sense. In this paper, we present a performance measure that estimates this distance without prior knowledge of the original image. Our measure relies on evaluating a spectral filter function at each step of the iteration. These functions describe the solution at each step in terms of the singular value decomposition of the system matrix. As such, spectral filter functions provide valuable insight into the behavior of an iteration as well as a means of defining a termination rule. We develop a general technique for determining the spectral filter functions for a given iteration, which we demonstrate by applying it to a linear iterative image restoration algorithm.