Digital Image Restoration Under a Regression Model - The Unconstrained, Linear Equality and Inequality Constrained Approaches
UNIVERSITY OF SOUTHERN CALIFORNIA LOS ANGELES IMAGE PROCESSING INST
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The problem of restoring images degraded by blur and corrupted by noise is considered in this report. A discretization of the Fredholm integral equation of the first kind in a two dimensional form is performed. The overdetermined and underdetermined regression models are examined in detail, with particular attention to the problem of ill conditioning. The results of the restoration of simulated pictures under atmospheric turbulence and diffraction limited point spread functions are presented. A priori information in the form of deterministic constraints is proposed as a means to solve the ill conditioning problem. With linear equality constraints, a combination of estimation and hypothesis testing is used to decide if a reduction of the mean square error occurs upon the imposition of the restrictions. Experimental results show that more acceptable results are obtained in the restoration. Linear inequality constraints are incorporated by a quadratic programming formulation. The use of low nonnegativeness and upper bounds indicate a substantial improvement in the restoration, even for the ill conditioned situation.
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