Thursday, 12.2.2009, 11:30
We address the open engineering problem of blind separation of time/position varying mixtures.
We show that there exists a large family of such mixtures that are separable without having prior
information about the sources or the mixing system. Unlike studies concerned with instantaneous
or convolutive mixtures, we relax the very-restrictive, widely-used, constraint of stationary in
time and position, and deal with the more practical and difficult problem of a mixing system
(medium) that is varying in time/position. The generalized model that represents such MIMO
mixing systems incorporates an integral operator of time/position varying filtering, analogous
to the convolution integral (filter) widely used in the case of stationary systems.
Our generalized approach to blind separation of sources models a wide range of physical phenomena such as time/position varying attenuation of signals, Doppler effect, zooming, linear and non-linear stretching of images, as well as variable media of audio reverberations, RF multipath and local blur of images.
In our approach to the source separation, we use the staged sparse component analysis (SSCA) approach, in which we sparsify the mixtures as a preprocessing stage, estimate the mixing matrix in the first stage and then solve the inverse problem to restore the sources in the second stage. Time/position varying mixing systems induce many obstacles in the process of using the SSCA. We deal with the reasons for the introduction of these obstacles and present several methods for effective separation of such mixtures, which overcome these problems.
* PhD research under the supervision of Prof. Y.Y. Zeevi