Image Restoration by Multiscale Spatial Adaptive Regularization

An image restoration is a typically ill-posed problem. Generally, regulalization scheme is used to avoid this problem. As a regularization operator, classical methods adopt one which may produce a too much smooth image. Parametric Projection Filter which has an ability to deal with colored observation noise is one of them.

On the other hand, some methods based on a spatially adaptive regularization are proposed and successful in obtaining not so smooth one. However, it is assumed that observation noise is white, and the fidelity of images is not evaluated in the space of original images in these methods.

In this paper, we propose a new restoration method by which we can evaluate the fidelity of images in the space of original images and obtain not so smooth one. We also verify the efficacy of the method by some numerical experiments.