On the Theorem of Uniform Recovery of Random Sampling Matrices
2014 (English)In: IEEE Transactions on Information Theory, ISSN 0018-9448, Vol. 60, no 3, 1700-1710 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2014. Vol. 60, no 3, 1700-1710 p.
Bounded orthogonal systems, compressive sensing, effective sparsity, l(1)-minimization, random sampling matrices, restricted isometry property
Signal Processing Other Mathematics Computational Mathematics
IdentifiersURN: urn:nbn:se:kth:diva-141831DOI: 10.1109/TIT.2014.2300092ISI: 000331902400026ScopusID: 2-s2.0-84896839927OAI: oai:DiVA.org:kth-141831DiVA: diva2:698794
QC 201402282014-02-252014-02-252014-03-28Bibliographically approved