Minimax solution of inverse problems and deconvolution by mirror wavelet thresholding

Jerome Kalifa; Stephane G. Mallat; Bernard Rouge

doi:10.1117/12.366803

26 October 1999 Minimax solution of inverse problems and deconvolution by mirror wavelet thresholding

Jerome Kalifa, Stephane G. Mallat, Bernard Rouge

Proceedings Volume 3813, Wavelet Applications in Signal and Image Processing VII; (1999) https://doi.org/10.1117/12.366803
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

We consider ill-posed inverse problems where inverting the distortion of signals and images in presence of additive noise is numerically unstable. The properties of linear and non-linear diagonal estimators in an orthogonal basis lead to general conditions to build nearly minimax optimal thresholding estimators. The deconvolution of bounded variation signals and images is studied in further details, with an application to the deblurring of satellite images. Besides their optimality properties, a competition set by the French spatial agency (CNES) showed that this type of algorithms gives the best numerical results among all competing algorithms.

Citation Download Citation

Jerome Kalifa, Stephane G. Mallat, and Bernard Rouge "Minimax solution of inverse problems and deconvolution by mirror wavelet thresholding", Proc. SPIE 3813, Wavelet Applications in Signal and Image Processing VII, (26 October 1999); https://doi.org/10.1117/12.366803

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