Newton-Raphson Method and Stability of Nonlinear Information Image-Recovery Techniques

Abstract

We consider the Newton-Raphson method as a method for the numerical implementation of nonlinear information image-recovery techniques. The classical and generalized maximum-entropy methods (MEM) are compared from the viewpoint of their sensitivity to input-data errors. A comparison of the spectral condition values of the Jacobi matrices shows that the generalized method is much more stable to noise than the conventional method, which is in good agreement with the empirical results. Unlike the generalized method, the conventional procedure requires that regularizing terms be added to the minimized functional to improve the stability of the numerical algorithms.