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Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition (1993)
| Venue: | in Conference Record of The Twenty-Seventh Asilomar Conference on Signals, Systems and Computers |
| Citations: | 632 - 1 self |
BibTeX
@INPROCEEDINGS{Pati93orthogonalmatching,
author = {Y. C. Pati and R. Rezaiifar and P. S. Krishnaprasad},
title = {Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition},
booktitle = {in Conference Record of The Twenty-Seventh Asilomar Conference on Signals, Systems and Computers},
year = {1993},
pages = {1--3}
}
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Abstract
In this paper we describe a recursive algorithm to compute representations of functions with respect to nonorthogonal and possibly overcomplete dictionaries of elementary building blocks e.g. aiEne (wa.velet) frames. We propoeea modification to the Matching Pursuit algorithm of Mallat and Zhang (1992) that maintains full backward orthogonality of the residual (error) at every step and thereby leads to improved convergence. We refer to this modified algorithm as Orthogonal Matching Pursuit (OMP). It is shown that all additional computation required for the OMP al gorithm may be performed recursively. where fk is the current approximation, and Rkf the current residual (error). Using initial values ofR0f = 1, fo = 0, and k = 1, the MP algorithm is comprised of the following steps,.,.41) Compute the inner-products {(Rkf,z)}. (H) Find flki such that (III) Set, I(R*f,1:n 1+,)l asupl(Rkf,z,)I, where 0 < a < 1. 1
Keyphrases
recursive function approximation find flki orthogonal matching pursuit mp algorithm initial value matching pursuit algorithm following step recursive algorithm omp al gorithm elementary building block full backward orthogonality additional computation overcomplete dictionary current approximation
