771 research outputs found
New Coherence and RIP Analysis for Weak Orthogonal Matching Pursuit
In this paper we define a new coherence index, named the global 2-coherence,
of a given dictionary and study its relationship with the traditional mutual
coherence and the restricted isometry constant. By exploring this relationship,
we obtain more general results on sparse signal reconstruction using greedy
algorithms in the compressive sensing (CS) framework. In particular, we obtain
an improved bound over the best known results on the restricted isometry
constant for successful recovery of sparse signals using orthogonal matching
pursuit (OMP).Comment: arXiv admin note: substantial text overlap with arXiv:1307.194
CoSaMP: Iterative signal recovery from incomplete and inaccurate samples
Compressive sampling offers a new paradigm for acquiring signals that are
compressible with respect to an orthonormal basis. The major algorithmic
challenge in compressive sampling is to approximate a compressible signal from
noisy samples. This paper describes a new iterative recovery algorithm called
CoSaMP that delivers the same guarantees as the best optimization-based
approaches. Moreover, this algorithm offers rigorous bounds on computational
cost and storage. It is likely to be extremely efficient for practical problems
because it requires only matrix-vector multiplies with the sampling matrix. For
many cases of interest, the running time is just O(N*log^2(N)), where N is the
length of the signal.Comment: 30 pages. Revised. Presented at Information Theory and Applications,
31 January 2008, San Dieg
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