Comparative Experimental Exploration of Robust Norm Functions for Iterative Super Resolution Reconstructions under Noise Surrounding

Abstract

In DIP (Digital Image Processing) research society, the multi-frame SRR (Super Resolution Reconstruction) algorithm has grown to be the momentous theme in the last ten years because of its cost e ectiveness and its superior spectacle. Consequently, for a multi-frame SRR algorithm which is commonly comprised of a Bayesian ML (Maximum Likelihood) approach and a regularization technique into the unify SRR framework, numerous robust norm functions (which have both redescending and non-redescending in uence functions) have been commonly comprised in the unify SRR framework for increasingly against noise or outlier. First, this paper presents the mathematical model of several iterative SRR based on a Bayesian ML (Maximum Likelihood) approach and a regularization technique. Three groups of robust norm functions (a zero-redescending in uence function (Tukey's Biweight, Andrew's Sine and Hampel), a nonzero-redescending in uence function (Lorentzian, Leclerc, Geman&McClure, Myriad and Meridian) and a non-redescending in uence function (Huber)) are mathematically incorporated into the SRR framework. The close form solutions of the SRR framework based on these robust norm functions have been concluded. Later, the experimental section utilizes two standard images of Lena and Susie (40th) for pilot studies and fraudulent noise patterns of noiseless, AWGN, Poisson, Salt&Pepper, and Speckle of several magnitudes used to contaminate these two standard images. In order to acquire the maximum PSNR, the comparative experimental exploration has been done by comprehensively tailoring all experimental parameters such as step-size, regularization parameter, norm constant parameter.