On the application of robust functionals in regularized image restoration

The authors address aspects of robust estimation in regularized image restoration, with the utilization of nonquadratic objective functions. The structural flexibility of generalized maximum-likelihood functions and M-estimators is exploited to provide accurate representation of a wide class of posterior (noise) distribution functions. The utilization of nonquadratic smoothing functionals for the restoration of sharp edges is addressed. In the context of robust estimation, the authors introduce novel entropic functionals that operate on a high-pass version of the original image and can accurately characterize a wide ensemble of images. The entropic functionals permit large signal deviations and enable the reconstruction of sharp edges. The properties of the robust algorithms are demonstrated through restoration examples in different noise environments.<>