dorsal/arxiv
View SchemaWavelet Domain Image Separation
| Authors | Ali Mohammad-Djafari, Mahieddine Ichir |
|---|---|
| Categories | |
| ArXiv ID | physics/0211052 |
| URL | https://arxiv.org/abs/physics/0211052 |
| DOI | 10.1063/1.1570545 |
Abstract
In this paper, we consider the problem of blind signal and image separation using a sparse representation of the images in the wavelet domain. We consider the problem in a Bayesian estimation framework using the fact that the distribution of the wavelet coefficients of real world images can naturally be modeled by an exponential power probability density function. The Bayesian approach which has been used with success in blind source separation gives also the possibility of including any prior information we may have on the mixing matrix elements as well as on the hyperparameters (parameters of the prior laws of the noise and the sources). We consider two cases: first the case where the wavelet coefficients are assumed to be i.i.d. and second the case where we model the correlation between the coefficients of two adjacent scales by a first order Markov chain. This paper only reports on the first case, the second case results will be reported in a near future. The estimation computations are done via a Monte Carlo Markov Chain (MCMC) procedure. Some simulations show the performances of the proposed method. Keywords: Blind source separation, wavelets, Bayesian estimation, MCMC Hasting-Metropolis algorithm.
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"abstract": "In this paper, we consider the problem of blind signal and image separation\nusing a sparse representation of the images in the wavelet domain. We consider\nthe problem in a Bayesian estimation framework using the fact that the\ndistribution of the wavelet coefficients of real world images can naturally be\nmodeled by an exponential power probability density function. The Bayesian\napproach which has been used with success in blind source separation gives also\nthe possibility of including any prior information we may have on the mixing\nmatrix elements as well as on the hyperparameters (parameters of the prior laws\nof the noise and the sources). We consider two cases: first the case where the\nwavelet coefficients are assumed to be i.i.d. and second the case where we\nmodel the correlation between the coefficients of two adjacent scales by a\nfirst order Markov chain. This paper only reports on the first case, the second\ncase results will be reported in a near future. The estimation computations are\ndone via a Monte Carlo Markov Chain (MCMC) procedure. Some simulations show the\nperformances of the proposed method. Keywords: Blind source separation,\nwavelets, Bayesian estimation, MCMC Hasting-Metropolis algorithm.",
"arxiv_id": "physics/0211052",
"authors": [
"Ali Mohammad-Djafari",
"Mahieddine Ichir"
],
"categories": [
"physics.data-an"
],
"doi": "10.1063/1.1570545",
"title": "Wavelet Domain Image Separation",
"url": "https://arxiv.org/abs/physics/0211052"
},
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