650 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
Improving A*OMP: Theoretical and Empirical Analyses With a Novel Dynamic Cost Model
Best-first search has been recently utilized for compressed sensing (CS) by
the A* orthogonal matching pursuit (A*OMP) algorithm. In this work, we
concentrate on theoretical and empirical analyses of A*OMP. We present a
restricted isometry property (RIP) based general condition for exact recovery
of sparse signals via A*OMP. In addition, we develop online guarantees which
promise improved recovery performance with the residue-based termination
instead of the sparsity-based one. We demonstrate the recovery capabilities of
A*OMP with extensive recovery simulations using the adaptive-multiplicative
(AMul) cost model, which effectively compensates for the path length
differences in the search tree. The presented results, involving phase
transitions for different nonzero element distributions as well as recovery
rates and average error, reveal not only the superior recovery accuracy of
A*OMP, but also the improvements with the residue-based termination and the
AMul cost model. Comparison of the run times indicate the speed up by the AMul
cost model. We also demonstrate a hybrid of OMP and A?OMP to accelerate the
search further. Finally, we run A*OMP on a sparse image to illustrate its
recovery performance for more realistic coefcient distributions
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