A Simple Proof of the Mutual Incoherence Condition for Orthogonal Matching Pursuit

Details A Simple Proof of the Mutual Incoherence Condition for Orthogonal Matching Pursuit A Simple Proof of the Mutual Incoherence Condition for Orthogonal Matching Pursuit

2011-05-23

arxiv.org/abs/1105.4408v1

Computer Science

Information Theory

8 pages

Scientific paper

This paper provides a simple proof of the mutual incoherence condition $\mu < \frac{1}{2K-1}$ under which K-sparse signal can be accurately reconstructed from a small number of linear measurements using the orthogonal matching pursuit (OMP) algorithm. Our proof, based on mathematical induction, is built on an observation that the general step of the OMP process is in essence same as the initial step since the residual is considered as a new measurement preserving the sparsity level of an input vector.

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