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On the Theorem of Uniform Recovery of Random Sampling MatricesPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2014 (English)In: IEEE Transactions on Information Theory, ISSN 0018-9448, E-ISSN 1557-9654, Vol. 60, no 3, p. 1700-1710Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2014. Vol. 60, no 3, p. 1700-1710
##### Keywords [en]

Bounded orthogonal systems, compressive sensing, effective sparsity, l(1)-minimization, random sampling matrices, restricted isometry property
##### National Category

Signal Processing Other Mathematics Computational Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-141831DOI: 10.1109/TIT.2014.2300092ISI: 000331902400026Scopus ID: 2-s2.0-84896839927OAI: oai:DiVA.org:kth-141831DiVA, id: diva2:698794
#####

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##### Note

##### In thesis

We consider two theorems from the theory of compressive sensing. Mainly a theorem concerning uniform recovery of random sampling matrices, where the number of samples needed in order to recover an s-sparse signal from linear measurements (with high probability) is known to be m greater than or similar to s(ln s)(3) ln N. We present new and improved constants together with what we consider to be a more explicit proof. A proof that also allows for a slightly larger class of m x N-matrices, by considering what is called effective sparsity. We also present a condition on the so-called restricted isometry constants, delta s, ensuring sparse recovery via l(1)-minimization. We show that delta(2s) < 4/root 41 is sufficient and that this can be improved further to almost allow for a sufficient condition of the type delta(2s) < 2/3.

QC 20140228

Available from: 2014-02-25 Created: 2014-02-25 Last updated: 2017-12-05Bibliographically approved1. On Invertibility of the Radon Transform and Compressive Sensing$(function(){PrimeFaces.cw("OverlayPanel","overlay698802",{id:"formSmash:j_idt738:0:j_idt742",widgetVar:"overlay698802",target:"formSmash:j_idt738:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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