Bayesian multichannel blind separation and deconvolution of images with application to document analysis

In this paper we apply Bayesian blind source separation (BSS) from noisy convolutive mixtures to jointly separate and restore source images degraded through unknown blur operators, and then linearly mixed. We found that this problem arises in several image processing applications, among which there are some interesting instances of degraded document analysis. In particular, the convolutive mixture model is proposed for describing multiple views of documents affected by the overlapping of two or more text patterns. We consider two different models, the interchannel model, where the data represents multispectral views of a single sided document, and the intrachannel model, where the data is given by two sets of multispectral views of the recto and verso side of a document page. In both cases, the aim of the analysis is to recover clean maps of the main foreground text, but also the enhancement and extraction of other document features, such as faint or masked patterns. We adopt Bayesian estimation for all the unknowns, and describe the typical local correlation within the individual source images through the use of suitable Gibbs priors, accounting also for well-behaved edges in the images. This a priori information is particularly suitable for the kind of objects depicted in the images treated, i.e. homogeneous texts in homogeneous background, and, as such, is capable to stabilize the ill-posed, inverse problem considered. The method is validated through numerical and real experiments that are representative of various real scenarios.