Wavelet domain image restoration with adaptive edge-preserving regularization

1 April 2000

journal article
Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Image Processing

Vol. 9 (4) , 597-608
https://doi.org/10.1109/83.841937

Abstract

In this paper, we consider a wavelet based edge-preserving regularization scheme for use in linear image restoration problems. Our efforts build on a collection of mathematical results indicating that wavelets are especially useful for representing functions that contain discontinuities (i.e., edges in two dimensions or jumps in one dimension). We interpret the resulting theory in a statistical signal processing framework and obtain a highly flexible framework for adapting the degree of regularization to the local structure of the underlying image. In particular, we are able to adapt quite easily to scale-varying and orientation-varying features in the image while simultaneously retaining the edge preservation properties of the regularizer. We demonstrate a half-quadratic algorithm for obtaining the restorations from observed data.

Keywords

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