A Measurement Rate-MSE Tradeoff for Compressive Sensing Through Partial Support Recovery
2014 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 62, no 18, 4643-4658 p.Article in journal (Refereed) Published
We study the fundamental relationship between two relevant quantities in compressive sensing: the measurement rate, which characterizes the asymptotic behavior of the dimensions of the measurement matrix in terms of the ratio m/ log n (m being the number of measurements and n the dimension of the sparse signal), and the mean square estimation error. First, we use an information-theoretic approach to derive sufficient conditions on the measurement rate to reliably recover a part of the support set that represents a certain fraction of the total signal power when the sparsity level is fixed. Second, we characterize the mean square error of an estimator that uses partial support set information. Using these two parts, we derive a tradeoff between the measurement rate and the mean square error. This tradeoff is achievable using a two-step approach: first support set recovery, then estimation of the active components. Finally, for both deterministic and random signals, we perform a numerical evaluation to verify the advantages of the methods based on partial support set recovery.
Place, publisher, year, edition, pages
IEEE Signal Processing Society, 2014. Vol. 62, no 18, 4643-4658 p.
Compressive sensing, sparse signal, support recovery, MSE, performance tradeoff
IdentifiersURN: urn:nbn:se:kth:diva-144414DOI: 10.1109/TSP.2014.2321739ISI: 000340847000001ScopusID: 2-s2.0-84906483401OAI: oai:DiVA.org:kth-144414DiVA: diva2:714923
FunderEU, FP7, Seventh Framework Programme, 257626
QC 201406172014-04-292014-04-222014-09-18Bibliographically approved