Open Access
2010 Stein block thresholding for wavelet-based image deconvolution
Christophe Chesneau, Jalal Fadili, Jean-Luc Starck
Electron. J. Statist. 4: 415-435 (2010). DOI: 10.1214/09-EJS550


In this paper, we propose a fast image deconvolution algorithm that combines adaptive block thresholding and Vaguelet-Wavelet Decomposition. The approach consists in first denoising the observed image using a wavelet-domain Stein block thresholding, and then inverting the convolution operator in the Fourier domain. Our main theoretical result investigates the minimax rates over Besov smoothness spaces, and shows that our block estimator can achieve the optimal minimax rate, or is at least nearly-minimax in the least favorable situation. The resulting algorithm is simple to implement and fast. Its computational complexity is dominated by that of the FFT. We report a simulation study to support our theoretical findings. The practical performance of our block vaguelet-wavelet deconvolution compares very favorably to existing competitors on a large set of test images.


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Christophe Chesneau. Jalal Fadili. Jean-Luc Starck. "Stein block thresholding for wavelet-based image deconvolution." Electron. J. Statist. 4 415 - 435, 2010.


Published: 2010
First available in Project Euclid: 29 April 2010

zbMATH: 1329.62392
MathSciNet: MR2645491
Digital Object Identifier: 10.1214/09-EJS550

Primary: 62F12 , 62M10
Secondary: 62F12

Keywords: block thresholding , Image deconvolution , LaTeX2e , minimax , Wavelets

Rights: Copyright © 2010 The Institute of Mathematical Statistics and the Bernoulli Society

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