Image Restoration with an Affine Constraint

A. Tanaka, H. Imai, and M. Miyakoshi (Japan)


image processing, image restoration, affine constraint, parametric partial projection filter


In image restoration problems, an effective restoration is achieved by a priori knowledge of the unknown original image. An affine constraint could be considered as such a priori knowledge, which may appear when we know inten sities of particular pixels of the unknown original image, for instance. Adopting the least-squares criterion with an affine constraint seems to be one of simple and reasonable approaches. However, it was reported in past studies that some problems may occur with the least-squares criterion based methods, even if no constraint is imposed. The fam ily of (parametric) projection filters was proposed as one of resolutions for the problems. However, they do not have a framework to deal with an affine constraint, while a linear constraint can be considered. In this paper, we propose a new restoration filter in which an affine constraint is appro priately considered by extending the (parametric) partial projection filter which belongs to the family of (parametric) projection filters. Numerical examples are also presented to verify the efficacy of the proposed method.

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