Comparative Experimental Exploration of Robust Norm Functions for Iterative Super Resolution Reconstructions under Noise Surrounding
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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 effectiveness 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 influence 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 Bayesian ML (Maximum Likelihood) approach and a regularization technique. Three groups of robust norm functions (a zero-redescending influence function (Tukey’s Biweight, Andrew’s Sine and Hampel), a nonzero-redescending influence function (Lorentzian, Leclerc, Geman&McClure, Myriad and Meridian) and a non-redescending influence 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 are 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.
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