Deconvolution by thresholding in mirror wavelet bases

Author

Kalifa, Jerome ; Mallat, Stephane ; Rouge, Bernard

Author_Institution

Centre de Math. Appliquees, Ecole Polytechnique, Palaiseau, France

Volume

12

Issue

4

fYear

2003

fDate

4/1/2003 12:00:00 AM

Firstpage

446

Lastpage

457

Abstract

The deconvolution of signals is studied with thresholding estimators that decompose signals in an orthonormal basis and threshold the resulting coefficients. A general criterion is established to choose the orthonormal basis in order to minimize the estimation risk. Wavelet bases are highly sub-optimal to restore signals and images blurred by a low-pass filter whose transfer function vanishes at high frequencies. A new orthonormal basis called mirror wavelet basis is constructed to minimize the risk for such deconvolutions. An application to the restoration of satellite images is shown.

Keywords

deconvolution; filtering theory; image restoration; low-pass filters; transfer functions; wavelet transforms; estimation risk. minimization; high frequencies; image deblurring; inverse problem; low-pass filter; mirror wavelet bases; mirror wavelet basis; orthonormal basis; satellite image restoration; signal decomposition; signal deconvolution; signal restoration; sub-optimal wavelet bases; thresholding estimators; transfer function; Deconvolution; Frequency; Image restoration; Low pass filters; Mirrors; Optical filters; Optical noise; Satellites; Signal restoration; Transfer functions;

fLanguage

English

Journal_Title

Image Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7149

Type

jour

DOI

10.1109/TIP.2003.810592

Filename

1201126