Generalized Null Space and Restricted Isometry Properties

Abstract : We propose a theoretical study of the conditions guar- anteeing 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.
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Submitted on : Wednesday, April 10, 2013 - 10:00:35 PM
Last modification on : Thursday, December 13, 2018 - 8:02:02 PM
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Tomer Peleg, Rémi Gribonval, Mike E. Davies. Generalized Null Space and Restricted Isometry Properties. Signal Processing with Adaptive Sparse Structured Representations 2013 (2013), EPFL, Jul 2013, Lausanne, Switzerland. ⟨hal-00811673⟩

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