17th International Symposium on
Mathematical Theory of Networks and Systems
Kyoto International Conference Hall, Kyoto, Japan, July 24-28, 2006

MTNS 2006 Paper Abstract

Close

Paper TuP13.1

Fuchs, Jean Jacques (Univ. de Rennes 1)

Sparse Representations and Realization Theory

Scheduled for presentation during the Regular Session "Linear Systems I" (TuP13), Tuesday, July 25, 2006, 15:20−15:45, Room 101

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on May 19, 2024

Keywords Linear systems, Filtering and estimation

Abstract

We present some results obtained recently in signal processing in the so-called ``sparse representations'' domain and indicate how they can be applied to a very specific and limited problem in realization theory. This is mainly to bring these type of results to the knowledge of this community. Other applications in order estimation for instance are potentially feasible. The basic problem is the following: given a ($n$, $m$)-matrix $A$ with $m>n$ and a vector $b=Ax_o$ with $x_o$ having $p$ non-zero components, find sufficient conditions for $x_o$ to be the unique sparsest solution of $Ax=b$, the answer is a upper-bound on $p$ depending upon $A$. We present as application the realization of a partial covariance sequences.