BSS with corrupted data in transformed domains

Abstract

Most techniques of Blind Source Separation (BSS) are highly sensitive to the presence of gross errors while these last are ubiquitous in many real-world applications. This mandates the development of robust BSS methods, especially to handle the determined case for which there is currently no strategy able to separate the outliers from the sources contributions. We propose a new method which exploits the difference of structural contents that is naturally exhibited by the sources and the outliers in many applications to accurately separate the two contributions. More precisely, we exploit the sparse representations of the signals in two adapted and different dictionaries to estimate jointly the mixing matrix, the sources and the outliers. Preliminary results show the good accuracy of the proposed algorithm in various settings.