dorsal/arxiv
View SchemaMCMC joint separation and segmentation of hidden Markov fields
| Authors | Hichem Snoussi, Ali Mohammad-Djafari |
|---|---|
| Categories | |
| ArXiv ID | physics/0211051 |
| URL | https://arxiv.org/abs/physics/0211051 |
Abstract
In this contribution, we consider the problem of the blind separation of noisy instantaneously mixed images. The images are modelized by hidden Markov fields with unknown parameters. Given the observed images, we give a Bayesian formulation and we propose to solve the resulting data augmentation problem by implementing a Monte Carlo Markov Chain (MCMC) procedure. We separate the unknown variables into two categories: 1. The parameters of interest which are the mixing matrix, the noise covariance and the parameters of the sources distributions. 2. The hidden variables which are the unobserved sources and the unobserved pixels classification labels. The proposed algorithm provides in the stationary regime samples drawn from the posterior distributions of all the variables involved in the problem leading to a flexibility in the cost function choice. We discuss and characterize some problems of non identifiability and degeneracies of the parameters likelihood and the behavior of the MCMC algorithm in this case. Finally, we show the results for both synthetic and real data to illustrate the feasibility of the proposed solution. keywords: MCMC, blind source separation, hidden Markov fields, segmentation, Bayesian approach
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"date_modified": "2026-03-02T18:00:42.614000Z",
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"abstract": "In this contribution, we consider the problem of the blind separation of\nnoisy instantaneously mixed images. The images are modelized by hidden Markov\nfields with unknown parameters. Given the observed images, we give a Bayesian\nformulation and we propose to solve the resulting data augmentation problem by\nimplementing a Monte Carlo Markov Chain (MCMC) procedure. We separate the\nunknown variables into two categories:\n 1. The parameters of interest which are the mixing matrix, the noise\ncovariance and the parameters of the sources distributions. 2. The hidden\nvariables which are the unobserved sources and the unobserved pixels\nclassification labels.\n The proposed algorithm provides in the stationary regime samples drawn from\nthe posterior distributions of all the variables involved in the problem\nleading to a flexibility in the cost function choice.\n We discuss and characterize some problems of non identifiability and\ndegeneracies of the parameters likelihood and the behavior of the MCMC\nalgorithm in this case.\n Finally, we show the results for both synthetic and real data to illustrate\nthe feasibility of the proposed solution. keywords: MCMC, blind source\nseparation, hidden Markov fields, segmentation, Bayesian approach",
"arxiv_id": "physics/0211051",
"authors": [
"Hichem Snoussi",
"Ali Mohammad-Djafari"
],
"categories": [
"physics.data-an"
],
"title": "MCMC joint separation and segmentation of hidden Markov fields",
"url": "https://arxiv.org/abs/physics/0211051"
},
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"variant": "snapshot-2026-03-01",
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