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A Bayesian grouplet transform

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Abstract

In the signal processing literature, wavelet transforms have been widely used for compression, restoration or texture processing. In this sense, grouplet transforms have been proposed to account for the geometrical image regularities. A grouplet transform (basis or frame) is based on an a priori fixed association field that groups image coefficients according to geometrical considerations. In this paper, we propose a method for estimating this association field in a Bayesian way. The resulting association field is therefore adaptive to the processed image content. A hierarchical Bayesian model is proposed and the inference is conducted using a Markov Chain Monte Carlo (MCMC) algorithm. The proposed method is tested on standard images in terms of association field quality and quantitative properties of the obtained wavelet coefficients. Specifically, the proposed method provides coefficients with low correlation level, and for which the highest level of energy is concentrated within the 20% most significant. These promising results confirm the potential of the proposed method for several image processing applications such as compression, denoising or restoration.

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Authors and Affiliations

  1. MIRACL laboratory, University of Sfax, Sfax, Tunisia

    Lotfi Chaari

  2. IRIT - INP-ENSEEIHT, University of Toulouse, Toulouse, France

    Lotfi Chaari

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  1. Lotfi Chaari
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Correspondence to Lotfi Chaari.

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Chaari, L. A Bayesian grouplet transform. SIViP 13, 871–878 (2019). https://doi.org/10.1007/s11760-019-01423-6

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  • DOI: https://doi.org/10.1007/s11760-019-01423-6

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