This is an announcement for the paper "Stability of low-rank matrix recovery and its connections to Banach space geometry" by Javier Alejandro Chavez-Dominguez and Denka Kutzarova.
Abstract: There are well-known relationships between compressed sensing and the geometry of the finite-dimensional $\ell_p$ spaces. A result of Kashin and Temlyakov can be described as a characterization of the stability of the recovery of sparse vectors via $\ell_1$-minimization in terms of the Gelfand widths of certain identity mappings between finite-dimensional $\ell_1$ and $\ell_2$ spaces, whereas a more recent result of Foucart, Pajor, Rauhut and Ullrich proves an analogous relationship even for $\ell_p$ spaces with $p < 1$. In this paper we prove what we call matrix or noncommutative versions of these results: we characterize the stability of low-rank matrix recovery via Schatten $p$-(quasi-)norm minimization in terms of the Gelfand widths of certain identity mappings between finite-dimensional Schatten $p$-spaces.
Archive classification: math.FA cs.IT math.IT
Remarks: 19 pages, 1 figure
Submitted from: jachavezd@math.utexas.edu
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1406.6712
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