A class of robust entropic functionals for image restoration

Abstract

This paper considers the concept of robust estimation in regularized image restoration. Robust functionals are employed for the representation of both the noise and the signal statistics. Such functionals allow the efficient suppression of a wide variety of noise processes and permit the reconstruction of sharper edges than their quadratic counterparts. A new class of robust entropic functionals is introduced, which operates only on the high-frequency content of the signal and reflects sharp deviations in the signal distribution. This class of functionals can also incorporate prior structural information regarding the original image, in a way similar to the maximum information principle. The convergence properties of robust iterative algorithms are studied for continuously and noncontinuously differentiable functionals. The definition of the robust approach is completed by introducing a method for the optimal selection of the regularization parameter. This method utilizes the structure of robust estimators that lack analytic specification. The properties of robust algorithms are demonstrated through restoration examples in different noise environments.