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Abstract: In many signal processing problems, it may be fruitful to represent thesignal under study in a frame. If a probabilistic approach is adopted, itbecomes then necessary to estimate the hyper-parameters characterizing theprobability distribution of the frame coefficients. This problem is difficultsince in general the frame synthesis operator is not bijective. Consequently,the frame coefficients are not directly observable. This paper introduces ahierarchical Bayesian model for frame representation. The posteriordistribution of the frame coefficients and model hyper-parameters is derived.Hybrid Markov Chain Monte Carlo algorithms are subsequently proposed to samplefrom this posterior distribution. The generated samples are then exploited toestimate the hyper-parameters and the frame coefficients of the target signal.Validation experiments show that the proposed algorithms provide an accurateestimation of the frame coefficients and hyper-parameters. Application topractical problems of image denoising show the impact of the resulting Bayesianestimation on the recovered signal quality.

Autor: L. Chaâri, J.-C. Pesquet, J.-Y. Tourneret, Ph. Ciuciu, A. Benazza-Benyahia

Fuente: https://arxiv.org/

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