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2008

A Frame Construction and a Universal Distortion Bound for Sparse Representations

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A Frame Construction and a Universal Distortion Bound for Sparse Representations
Abstract-- We consider approximations of signals by the elements of a frame in a complex vector space of dimension N and formulate both the noiseless and the noisy sparse representation problems. The noiseless representation problem is to find sparse representations of a signal r given that such representations exist. In this case, we explicitly construct a frame, referred to as the Vandermonde frame, for which the noiseless sparse representation problem can be solved uniquely using O(N2 ) operations, as long as the number of non-zero coefficients in the sparse representation of r is N for some 0 0.5. It is known that 0.5 cannot be relaxed without violating uniqueness. The noisy sparse representation problem is to find sparse representations of a signal r satisfying a distortion criterion. In this case, we establish a lower bound on the trade-off between the sparsity of the representation, the underlying distortion and the redundancy of any given frame.
Mehmet Akçakaya, Vahid Tarokh
Added 16 Dec 2010
Updated 16 Dec 2010
Type Journal
Year 2008
Where TSP
Authors Mehmet Akçakaya, Vahid Tarokh
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