Geometric Conditions for Subspace-Sparse Recovery

author: René Vidal, John Hopkins University
published: Sept. 27, 2015,   recorded: July 2015,   views: 1514
Categories

Related Open Educational Resources

Related content

Report a problem or upload files

If you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
Lecture popularity: You need to login to cast your vote.
  Bibliography

Description

Given a dictionary Π and a signal ξ=Πx generated by a few linearly independent columns of Π, classical sparse recovery theory deals with the problem of uniquely recovering the sparse representation x of ξ. In this work, we consider the more general case where ξ lies in a low-dimensional subspace spanned by a few columns of Π, which are possibly linearly dependent. In this case, x may not unique, and the goal is to recover any subset of the columns of Π that spans the subspace containing ξ. We call such a representation x subspace-sparse. We study conditions under which existing pursuit methods recover a subspace-sparse representation. Such conditions reveal important geometric insights and have implications for the theory of classical sparse recovery as well as subspace clustering.

Link this page

Would you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !

Write your own review or comment:

make sure you have javascript enabled or clear this field: