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Journal Articles Wiley Encyclopedia of Electrical and Electronics Engineering Year : 2016

Wavelet-based Image Deconvolution and Reconstruction


Image deconvolution and reconstruction are inverse problems which are encountered in a wide array of applications. Due to the ill-posedness of such problems, their resolution generally relies on the incorporation of prior information through regularizations, which may be formulated in the original data space or through a suitable linear representation. In this article, we show the benefits which can be drawn from frame representations, such as wavelet transforms. We present an overview of recovery methods based on these representations: (i) variational formulations and non-smooth convex optimization strategies, (ii) Bayesian approaches, especially Monte Carlo Markov Chain methods and variational Bayesian approximation techniques, and (iii) Stein-based approaches. A brief introduction to blind deconvolution is also provided.
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Dates and versions

hal-01164833 , version 1 (17-06-2015)
hal-01164833 , version 2 (23-09-2015)
hal-01164833 , version 3 (22-04-2016)
hal-01164833 , version 4 (21-10-2016)
hal-01164833 , version 5 (24-08-2017)


  • HAL Id : hal-01164833 , version 5


Nelly Pustelnik, Amel Benazza-Benhayia, Yuling Zheng, Jean-Christophe Pesquet. Wavelet-based Image Deconvolution and Reconstruction. Wiley Encyclopedia of Electrical and Electronics Engineering, 2016. ⟨hal-01164833v5⟩
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