| Paper: | SPTM-P1.6 | ||
| Session: | System Identification and Parameter Estimation | ||
| Time: | Tuesday, May 18, 13:00 - 15:00 | ||
| Presentation: | Poster | ||
| Topic: | Signal Processing Theory and Methods: System Modeling, Representation, & Identification | ||
| Title: | RECOVERY OF EXACT SPARSE REPRESENTATIONS IN THE PRESENCE OF NOISE. | ||
| Authors: | Jean-jacques Fuchs; IRISA/University de Rennes 1 | ||
| Abstract: | The purpose of this contribution is to extend some recent results onsparse representations of signals in redundant bases developed in the noise-free case to the case of noisy observations.The type of questions addressed so far is : given a (n,m)-matrix $A$ with $m>n$ and a vector $b=Ax$, find a sufficient condition for $b$ to have an unique sparsest representation as a linear combination of the columns of $A$. The answer is a bound on the number of non-zero entries of say $x_o$, that guaranties that $x_o$ is the uniqueand sparsest solution of $Ax=b$ with $b=Ax_o$. We consider the case $b=Ax_o+e$ where $x_o$ satisfies the sparsity conditions requested in the noise-free case and seek conditions on $e$, a vector of additive noise or modeling errors,under which $x_o$ can be recovered from $b$ in a sense to be defined. | ||
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