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Bayesian separation of images modeled with MRFs using MCMC.
Koray Kayabol1, Ercan E Kuruoğlu, Bülent Sankur
1Electrical and Electronics Engineering Department, Istanbul University, Istanbul, Turkey. koray.kayabol@isti.cnr.it
Summary
This study introduces a novel Bayesian approach for random field source separation, significantly outperforming existing methods. The technique effectively separates mixed signals using advanced Markov random fields and modified-Gibbs sampling.
Area of Science:
- Signal Processing
- Computational Imaging
- Statistical Modeling
Background:
- Source separation is crucial in various fields.
- Bayesian methods offer a robust framework for incorporating prior information.
- Existing methods like Iterated Conditional Modes (ICM) and Independent Component Analysis (ICA) have limitations.
Purpose of the Study:
- To develop a fully Bayesian method for random field source separation.
- To incorporate prior image models using Markov random fields.
- To outperform approximate Bayesian and non-Bayesian source separation techniques.
Main Methods:
- A Bayesian framework for source separation of random fields.
- Joint maximization of the a posteriori distribution using numerical methods.
- Markov random fields for prior pixel density estimation based on gradient image statistics.
- Fully Bayesian inference with modified-Gibbs sampling.
Main Results:
- The proposed Bayesian method significantly outperforms approximate Bayesian (ICM) and non-Bayesian (ICA) competitors.
- Effective source separation demonstrated on synthetic texture and astrophysical images.
- Robust performance across various noise scenarios.
Conclusions:
- The developed fully Bayesian approach provides superior performance for random field source separation.
- Incorporating prior image models via Markov random fields enhances estimation accuracy.
- This method offers a powerful alternative to existing source separation techniques.