Electronic Journal of Statistics

Stein block thresholding for wavelet-based image deconvolution

Christophe Chesneau, Jalal Fadili, and Jean-Luc Starck

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Statist. Volume 4 (2010), 415-435.

Dates
First available in Project Euclid: 29 April 2010

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1272547189

Digital Object Identifier
doi:10.1214/09-EJS550

Mathematical Reviews number (MathSciNet)
MR2645491

Zentralblatt MATH identifier
1329.62392

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62F12: Asymptotic properties of estimators
Secondary: 62F12: Asymptotic properties of estimators

Keywords
Image deconvolution block thresholding wavelets minimax LaTeX2e

Citation

Chesneau, Christophe; Fadili, Jalal; Starck, Jean-Luc. Stein block thresholding for wavelet-based image deconvolution. Electron. J. Statist. 4 (2010), 415--435. doi:10.1214/09-EJS550. https://projecteuclid.org/euclid.ejs/1272547189


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