On Formulations and Solutions in Linear Image Restoration Problems

Akira TANAKA  Hideyuki IMAI  Masaaki MIYAKOSHI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E87-A   No.8   pp.2144-2151
Publication Date: 2004/08/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Image
image restoration,  formulation of the optimality,  optimization criterion,  

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In terms of the formulation of the optimality, image restoration filters can be divided into two streams. One is formulated as an optimization problem in which the fidelity of a restored image is indirectly evaluated, and the other is formulated as an optimization problem based on a direct evaluation. Originally, the formulation of the optimality and the solutions derived from the formulation are identical each other. However in many studies adopting the former stream, an arbitrary choice of a solution without a mathematical ground passes unremarked. In this paper, we discuss the relation between the formulation of the optimality and the solution derived from the formulation from a mathematical point of view, and investigate the relation between a direct style formulation and an indirect one. Through these analyses, we show that the both formulations yield the identical filter in practical situations.