# Technical Report CIS-2008-07

 TR#: CIS-2008-07 Class: CIS Title: Using Joint Sparsity for Blind Separation of Noisy Multichannel Signals Authors: Grigory Begelman, Ehud Rivlin and Michael Zibulevsky PDF CIS-2008-07.pdf Abstract: We call a set of vectors $z[k]\in R^m$ jointly sparse, when for the most of them all $m$ components are simultaneously [close to] zero. When recovering this set from [indirect] noisy observations using variational approach, joint sparsity prior can be expressed via convex penalty term $\sum_k \|z[k]\|_2$. In this work we explore joint sparsity in the context of blind source separation problem $X=AS+\xi$, where mixing matrix $A$ is and sources $S$ are unknown. We suppose $S$ to have sparse representation coefficients $C$ in some given signal frame (dictionary) $\Phi$: $S=C\Phi$. In this case, the mixtures' coefficients $AC$ are jointly sparse, therefore we can recover them robustly without knowledge of mixing matrix $A$, just using joint sparsity prior and solving a convex optimization problem. Another use of joint sparsity comes when the sources themselves are not scalars, but vectors (for example, color images: three RGB color layers usually have spatial similarities, therefore their [wavelet-type] representations are jointly sparse.) Our simulations show efficiency of the presented approach. Copyright The above paper is copyright by the Technion, Author(s), or others. Please contact the author(s) for more information

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