This project aims to study of techniques relating to the use of the sparty of the signal in problems commonly called as blind source separation problems, where is desired to retrieve the sources of a mixture, in an unsupervised manner. In this sense, the study has two fronts. The first one is to perform source separation using the information that the signals are sparse in some domain, where it is intended to: a) understand the relationship between the characteristics of sparsity of the source signals and the mutual information between them, and how to relate the characteristics of sparsity and the problem of separation in underdetermined systems; b) propose new cost functions that can serve as contrast to recover and reconstruct the sources.The second part deal to sparsity in relation with decomposition of the signal in subspaces, and, in consequence, the source separation in situations where there is only one mixture. Thus, it is intended to: a) study the latest techniques proposed in this area, b) evaluate how to integrate these techniques to the proposed in the case where the number of mixtures is greater than one.As an application, the candidate intends to concentrate its efforts in two areas: audio and geophysical processing.
News published in Agência FAPESP Newsletter about the scholarship: