A Markov model for blind image separation by a mean-field EM algorithm

• Published in: IEEE transactions on image processing Vol. 15; no. 2; pp. 473 - 482
• Main Authors: Tonazzini, A., Bedini, L., Salerno, E.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.02.2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Artificial Intelligence; Autocorrelation; Bayesian methods; Blind source separation; Blind source separation (BSS); Blinds; Computer Simulation; edge and feature detection; Estimating; Exact sciences and technology; Expectation-maximization algorithms; Image edge detection; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image processing; Image reconstruction; Image restoration; Independent component analysis; Information Storage and Retrieval - methods; Information, signal and communications theory; Magnetorheological fluids; Markov Chains; Markov random fields; Markov random fields (MRFs); Mathematical models; Models, Statistical; parameter learning; Pattern Recognition, Automated - methods; Preserves; scene analysis; Separation; Signal processing; Signal Processing, Computer-Assisted; Studies; Subtraction Technique; Telecommunications and information theory; Testing; Source separation; Image processing; Markov random fields (MRFs); Blind identification; Markov model; Image restoration; Blind source separation (BSS); parameter learning; Random field; edge and feature detection; Scene analysis; Feature extraction; EM algorithm; Edge detection
• ISSN: 1057-7149; 1941-0042
• DOI: 10.1109/TIP.2005.860323

This paper deals with blind separation of images from noisy linear mixtures with unknown coefficients, formulated as a Bayesian estimation problem. This is a flexible framework, where any kind of prior knowledge about the source images and the mixing matrix can be accounted for. In particular, we describe local correlation within the individual images through the use of Markov random field (MRF) image models. These are naturally suited to express the joint pdf of the sources in a factorized form, so that the statistical independence requirements of most independent component analysis approaches to blind source separation are retained. Our model also includes edge variables to preserve intensity discontinuities. MRF models have been proved to be very efficient in many visual reconstruction problems, such as blind image restoration, and allow separation and edge detection to be performed simultaneously. We propose an expectation-maximization algorithm with the mean field approximation to derive a procedure for estimating the mixing matrix, the sources, and their edge maps. We tested this procedure on both synthetic and real images, in the fully blind case (i.e., no prior information on mixing is exploited) and found that a source model accounting for local autocorrelation is able to increase robustness against noise, even space variant. Furthermore, when the model closely fits the source characteristics, independence is no longer a strict requirement, and cross-correlated sources can be separated, as well.