Geometric Conditions for Subspace-Sparse Recovery
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چکیده
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 lowdimensional 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.
منابع مشابه
Subspace-Sparse Representation
Given an overcomplete dictionary A and a signal b that is a linear combination of a few linearly independent columns of A, classical sparse recovery theory deals with the problem of recovering the unique sparse representation x such that b = Ax. It is known that under certain conditions on A, x can be recovered by the Basis Pursuit (BP) and the Orthogonal Matching Pursuit (OMP) algorithms. In t...
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تاریخ انتشار 2015