Restricted q-Isometry properties adapted to frames for nonconvex lq -analysis

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Author(s)

  • Junhong Lin
  • Song Li

Related Research Unit(s)

Detail(s)

Original languageEnglish
Article number7479583
Pages (from-to)4733-4747
Journal / PublicationIEEE Transactions on Information Theory
Volume62
Issue number8
Online published26 May 2016
Publication statusPublished - Aug 2016

Abstract

This paper discusses the reconstruction of signals from few measurements in the situation that signals are sparse or approximately sparse in terms of a general frame via the lq -analysis optimization with 0q -analysis optimization. We then determine how many random Gaussian measurements are needed for the condition to hold with high probability. The resulting sufficient condition is met by fewer measurements for smaller q than when q=1. The introduced generalized q -RIP is also useful in compressed data separation. In compressed data separation, one considers the problem of reconstruction of signals' distinct subcomponents, which are (approximately) sparse in morphologically different dictionaries, from few measurements. With the notion of generalized q -RIP, we show that under a usual assumption that the dictionaries satisfy a mutual coherence condition, the lq split analysis with 0

Research Area(s)

  • $l-{q}$ -analysis, Compressed sensing, data separation, frames, restricted isometry property, sparse recovery

Citation Format(s)

Restricted q-Isometry properties adapted to frames for nonconvex lq -analysis. / Lin, Junhong; Li, Song.

In: IEEE Transactions on Information Theory, Vol. 62, No. 8, 7479583, 08.2016, p. 4733-4747.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review