OMP and Continuous Dictionaries: Is k-step Recovery Possible?

Clément Elvira; Rémi Gribonval; Charles Soussen; Cédric Herzet

ICASSP 2019accepted0 citations

OMP and Continuous Dictionaries: Is k-step Recovery Possible?

Clément Elvira, Rémi Gribonval, Charles Soussen, Cédric Herzet

Abstract

In this work, we present new theoretical results on sparse recovery guarantees for a greedy algorithm, orthogonal matching pursuit (OMP), in the context of continuous parametric dictionaries, i.e., made up of an infinite uncountable number of atoms. We build up a family of dictionaries for which k-step recovery is possible with OMP for 1-dimensional parameters. In higher dimension, algebraic conditions become necessary and will lead us to revisit some well-known k-step discrete analyses. Finally, a toy-example illustrates the level of tightness of our sufficient conditions.

BibTeX

@inproceedings{icassp2019_ompandcontinuous,
  title = {OMP and Continuous Dictionaries: Is k-step Recovery Possible?},
  author = {Clément Elvira and Rémi Gribonval and Charles Soussen and Cédric Herzet},
  booktitle = {ICASSP 2019},
  year = {2019}
}