Solution of inverse problems in image processing by wavelet expansion

Author

Wang, Gaofeng ; Zhang, Jun ; Pan, Guang-Wen

Author_Institution

Tanner Res. Inc., Pasadena, CA, USA

Volume

4

Issue

5

fYear

1995

fDate

5/1/1995 12:00:00 AM

Firstpage

579

Lastpage

593

Abstract

We describe a wavelet-based approach to linear inverse problems in image processing. In this approach, both the images and the linear operator to be inverted are represented by wavelet expansions, leading to a multiresolution sparse matrix representation of the inverse problem. The constraints for a regularized solution are enforced through wavelet expansion coefficients. A unique feature of the wavelet approach is a general and consistent scheme for representing an operator in different resolutions, an important problem in multigrid/multiresolution processing. This and the sparseness of the representation induce a multigrid algorithm. The proposed approach was tested on image restoration problems and produced good results

Keywords

image representation; image resolution; image restoration; inverse problems; matrix algebra; wavelet transforms; image processing; image representation; image resolution; image restoration; linear inverse problems; linear operator; multigrid algorithm; multigrid/multiresolution processing; multiresolution sparse matrix representation; wavelet expansion coefficients; Image processing; Image reconstruction; Image resolution; Image restoration; Inverse problems; Iterative methods; Motion estimation; Senior members; Sparse matrices; Testing;

fLanguage

English

Journal_Title

Image Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7149

Type

jour

DOI

10.1109/83.382493

Filename

382493