Deconvolution by thresholding in mirror wavelet bases

被引：35

作者：

Kalifa, J ^{[1
]}

Mallat, S

Rougé, B

机构：

[1] Ecole Polytech, Ctr Math Appl, F-91128 Palaiseau, France

[2] NYU, Courant Inst Math Sci, New York, NY 10012 USA

[3] Ctr Natl Etud Spatiales, F-31055 Toulouse, France

来源：

IEEE TRANSACTIONS ON IMAGE PROCESSING | 2003年 / 12卷 / 04期

基金：

美国国家科学基金会;

关键词：

deconvolution; inverse problem; thresholding; wavelet packets;

D O I：

10.1109/TIP.2003.810592

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

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.

引用

页码：446 / 457

页数：12

共 22 条

[1]

BERTERO M, 1989, ADV ELECT ELECT PHYS

[2] A generalized Gaussian image model for edge-preserving MAP estimation [J].

Bournan, Charles ;

Sauer, Ken .

IEEE TRANSACTIONS ON IMAGE PROCESSING, 1993, 2 (03) :296-310

[3] Image recovery via total variation minimization and related problems [J].

Chambolle, A ;

Lions, PL .

NUMERISCHE MATHEMATIK, 1997, 76 (02) :167-188

[4] Deterministic edge-preserving regularization in computed imaging [J].

Charbonnier, P ;

BlancFeraud, L ;

Aubert, G ;

Barlaud, M .

IEEE TRANSACTIONS ON IMAGE PROCESSING, 1997, 6 (02) :298-311

[5]

Coifman R., 1992, Proc. Wavelets and Their Applications, P153

[6]

COIFMAN R. R., 1995, Wavelets and statistics, P125, DOI DOI 10.1007/978-1-4612-2544-7_9

[7] IMAGE-RECONSTRUCTION AND RESTORATION - OVERVIEW OF COMMON ESTIMATION STRUCTURES AND PROBLEMS [J].

DEMOMENT, G .

IEEE TRANSACTIONS ON ACOUSTICS SPEECH AND SIGNAL PROCESSING, 1989, 37 (12) :2024-2036

[8] IDEAL SPATIAL ADAPTATION BY WAVELET SHRINKAGE [J].

DONOHO, DL ;

JOHNSTONE, IM .

BIOMETRIKA, 1994, 81 (03) :425-455

[9] NONLINEAR SOLUTION OF LINEAR INVERSE PROBLEMS BY WAVELET-VAGUELETTE DECOMPOSITION [J].

DONOHO, DL .

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 1995, 2 (02) :101-126

[10] CONSTRAINED RESTORATION AND THE RECOVERY OF DISCONTINUITIES [J].

GEMAN, D ;

REYNOLDS, G .

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 1992, 14 (03) :367-383

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