Unsupervised blind separation and debluring of mixtures of sources

Authors:
Livio Fedeli;Ivan Gerace;Francesca Martinelli
Affiliations:
Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy;Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy;Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy
Venue:
KES'07/WIRN'07 Proceedings of the 11th international conference, KES 2007 and XVII Italian workshop on neural networks conference on Knowledge-based intelligent information and engineering systems: Part III
Year:
2007

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Abstract

In this paper we consider the problem of separating source images from linear mixtures with unknown coefficients, in presence of noise and blur. In particular, we consider as a special case the problem of estimating the Cosmic Microwave Background from galactic and extra-galactic emissions. Like many visual inverse problems, this problem results to be ill-posed in Hadamard sense. To solve the nonblind version of the problem a classical edge-preserving regularization technique can be used. Thus, the solution is defined as the argument of the minimum of an energy function. In order to solve the blind inverse problem, in this paper a new function, called target function, is introduced. Such a function can consider constraints as the degree of Gaussianity and correlation of the results. The experimental results, considering the cosmic mixtures, have given accurate estimations.