Unsupervised image restoration and edge location using compound Gauss-Markov random fields and the MDL principle

• Published in: IEEE transactions on image processing Vol. 6; no. 8; pp. 1089 - 1102
• Main Authors: Figueiredo, M.A.T., Leitao, J.M.N.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.1997; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Bayesian methods; Constraint theory; Estimation theory; Exact sciences and technology; Gaussian processes; Image edge detection; Image processing; Image reconstruction; Image restoration; Information, signal and communications theory; Iterative algorithms; Markov random fields; Signal processing; Telecommunications and information theory; Testing; Discontinuity; Parameter estimation; Experimental result; Image processing; Gaussian field; Minimum principle; Markov model; Image restoration; Localization; Algorithm; Edge detection
• ISSN: 1057-7149; 1941-0042
• DOI: 10.1109/83.605407

Discontinuity-preserving Bayesian image restoration typically involves two Markov random fields: one representing the image intensities/gray levels to be recovered and another one signaling discontinuities/edges to be preserved. The usual strategy is to perform joint maximum a posterori (MAP) estimation of the image and its edges, which requires the specification of priors for both fields. Instead of taking an edge prior, we interpret discontinuities (in fact their locations) as deterministic unknown parameters of the compound Gauss-Markov random field (CGMRF), which is assumed to model the intensities. This strategy should allow inferring the discontinuity locations directly from the image with no further assumptions. However, an additional problem emerges: the number of parameters (edges) is unknown. To deal with it, we invoke the minimum description length (MDL) principle; according to MDL, the best edge configuration is the one that allows the shortest description of the image and its edges. Taking the other model parameters (noise and CGMRF variances) also as unknown, we propose a new unsupervised discontinuity-preserving image restoration criterion. Implementation is carried out by a continuation-type iterative algorithm which provides estimates of the number of discontinuities, their locations, the noise variance, the original image variance, and the original image itself (restored image). Experimental results with real and synthetic images are reported.