 Info
Stability of lowrank matrix recovery and its connections to Banach space geometry
J. Alejandro Chavez Dominguez, University of Oklahoma
What 

When 
Fri, Feb 24, 2017
from
11:00 AM
to
11:50 AM

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Abstract:
Compressed sensing deals with the problem of recovering a vector in a highdimensional space from a lowerdimensional measurement, under the assumption that the vector is sparse (that is, it has relatively few nonzero coordinates). One of the bestknown techniques to achieve such recovery is the $\ell_p$norm minimization, and its properties are related to the geometry of the Banach spaces involved: theorems by KashinTemlyakov and FoucartPajorRauhutUllrich relate the stability of sparse vector recovery via $\ell_p$minimization to the socalled Gelfand numbers of identity maps between finitedimensional $\ell_p$spaces.
In many practical situations the space of unknown vectors has in fact a matrix structure, a good example being the famous matrix completion problem (also known as the Netflix problem) where the unknown is a matrix and we are given a subset of its entries. In this case sparsity gets replaced by the more natural condition of having low rank, and the last few years have witnessed an explosion of work in this area. In this talk we present matrix analogues of the aforementioned results, relating the stability of lowrank matrix recovery via Schatten $p$minimization to the Gelfand numbers of identity maps between finitedimensional Schatten $p$spaces.


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