@inproceedings{5eb82f3e58b04b8895f7eee64f870d29,
title = "Compressed sensing and best approximation from unions of subspaces: Beyond dictionaries",
abstract = "We propose a theoretical study of the conditions guaranteeing that a decoder will obtain an optimal signal recovery from an underdetermined set of linear measurements. This special type of performance guarantee is termed instance optimality and is typically related with certain properties of the dimensionality-reducing matrix M. Our work extends traditional results in sparse recovery, where instance optimality is expressed with respect to the set of sparse vectors, by replacing this set with an arbitrary finite union of subspaces. We show that the suggested instance optimality is equivalent to a generalized null space property of M and discuss possible relations with generalized restricted isometry properties.",
keywords = "Instance optimality, null space property, restricted isometry property, union-of-subspaces",
author = "Tomer Peleg and Remi Gribonval and Davies, {Mike E.}",
year = "2013",
month = jan,
day = "1",
language = "English",
isbn = "9780992862602",
series = "European Signal Processing Conference",
publisher = "European Signal Processing Conference, EUSIPCO",
booktitle = "2013 Proceedings of the 21st European Signal Processing Conference, EUSIPCO 2013",
note = "2013 21st European Signal Processing Conference, EUSIPCO 2013 ; Conference date: 09-09-2013 Through 13-09-2013",
}