Optimal D -RIP bounds in compressed sensing
| LEADER | caa a22 4500 | ||
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| 001 | 605462038 | ||
| 003 | CHVBK | ||
| 005 | 20210128100246.0 | ||
| 007 | cr unu---uuuuu | ||
| 008 | 210128e20150501xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s10114-015-4234-4 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10114-015-4234-4 | ||
| 245 | 0 | 0 | |a Optimal D -RIP bounds in compressed sensing |h [Elektronische Daten] |c [Rui Zhang, Song Li] |
| 520 | 3 | |a This paper establishes new bounds on the restricted isometry constants with coherent tight frames in compressed sensing. It is shown that if the sensing matrix A satisfies the D-RIP condition δ k < 1/3 or $$\delta _{2k} < \sqrt 2 /2$$ , then all signals f with D*f are k-sparse can be recovered exactly via the constrained ℓ 1 minimization based on y = Af, where D* is the conjugate transpose of a tight frame D. These bounds are sharp when D is an identity matrix, see Cai and Zhang's work. These bounds are greatly improved comparing to the condition δ k < 0.307 or δ 2k < 0.4931. Besides, if δ k < 1/3 or $$\delta _{2k} < \sqrt 2 /2$$ , the signals can also be stably reconstructed in the noisy cases. | |
| 540 | |a Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg, 2015 | ||
| 690 | 7 | |a Compressed sensing |2 nationallicence | |
| 690 | 7 | |a D -restricted isometry property |2 nationallicence | |
| 690 | 7 | |a coherent |2 nationallicence | |
| 690 | 7 | |a tight frames |2 nationallicence | |
| 700 | 1 | |a Zhang |D Rui |u Department of Mathematics, Zhejiang University, 310027, Hangzhou, P. R. China |4 aut | |
| 700 | 1 | |a Li |D Song |u Department of Mathematics, Zhejiang University, 310027, Hangzhou, P. R. China |4 aut | |
| 773 | 0 | |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/5(2015-05-01), 755-766 |x 1439-8516 |q 31:5<755 |1 2015 |2 31 |o 10114 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10114-015-4234-4 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10114-015-4234-4 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Zhang |D Rui |u Department of Mathematics, Zhejiang University, 310027, Hangzhou, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Li |D Song |u Department of Mathematics, Zhejiang University, 310027, Hangzhou, P. R. China |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Acta Mathematica Sinica, English Series |d Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society |g 31/5(2015-05-01), 755-766 |x 1439-8516 |q 31:5<755 |1 2015 |2 31 |o 10114 | ||