Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies?
| dc.creator | Candes, Emmanuel | |
| dc.creator | Tao, Terence | |
| dc.date | 2004-10-25 | |
| dc.date | 2006-04-04 | |
| dc.date.accessioned | 2026-07-07T06:38:57Z | |
| dc.date.available | 2026-07-07T06:38:57Z | |
| dc.description | Suppose we are given a vector $f$ in $\R^N$. How many linear measurements do we need to make about $f$ to be able to recover $f$ to within precision $ε$ in the Euclidean ($\ell_2$) metric? Or more exactly, suppose we are interested in a class ${\cal F}$ of such objects--discrete digital signals, images, etc; how many linear measurements do we need to recover objects from this class to within accuracy $ε$? This paper shows that if the objects of interest are sparse or compressible in the sense that the reordered entries of a signal $f \in {\cal F}$ decay like a power-law (or if the coefficient sequence of $f$ in a fixed basis decays like a power-law), then it is possible to reconstruct $f$ to within very high accuracy from a small number of random measurements. | |
| dc.description | 39 pages; no figures; to appear. Bernoulli ensemble proof has been corrected; other expository and bibliographical changes made, incorporating referee's suggestions | |
| dc.identifier | https://arxiv.org/abs/math/0410542 | |
| dc.identifier | http://arxiv.org/abs/math/0410542 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100918 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Probability | |
| dc.subject | 47B06; 42A10; 41A45; 65A99 | |
| dc.title | Near Optimal Signal Recovery From Random Projections: Universal Encoding Strategies? | |
| dc.type | text |