Stability of low-rank matrix recovery and its connections to Banach space geometry

作者：Chavez Dominguez Javier Alejandro^*; Kutzarova Denka

来源：Journal of Mathematical Analysis and Applications, 2015, 427(1): 320-335.

DOI：10.1016/j.jmaa.2015.02.041

• Compressed sensing
• Low-rank matrix recovery
• Schatten p-minimization
• Gelfand widths

There are well-known relationships between compressed sensing and the geometry of the finite-dimensional l(p) spaces. A result of Kashin and Temlyakov [20] can be described as a characterization of the stability of the recovery of sparse vectors via l(1)-minimization in terms of the Gelfand widths of certain identity mappings between finite-dimensional l(1) and l(2) spaces, whereas a more recent result of Foucart, Pajor, Rauhut and Ullrich [16] proves an analogous relationship even for l(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.

• 出版日期2015-7-1