Name
Title | ||
|---|---|---|
Sobolev Duals for Random Frames and ΣΔ Quantization of Compressed Sensing Measurements |
Abstract | ||
|---|---|---|
AbstractQuantization of compressed sensing measurements is typically justified by the robust recovery results of Candès, Romberg and Tao, and of Donoho. These results guarantee that if a uniform quantizer of step size ź is used to quantize m measurements y=źx of a k-sparse signal xźźN, where ź satisfies the restricted isometry property, then the approximate recovery x# via ℓ1-minimization is within O(ź) of x. The simplest and commonly assumed approach is to quantize each measurement independently. In this paper, we show that if instead an rth-order ΣΔ (Sigma---Delta) quantization scheme with the same output alphabet is used to quantize y, then there is an alternative recovery method via Sobolev dual frames which guarantees a reduced approximation error that is of the order ź(k/m)(rź1/2)ź for any 0 |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1007/s10208-012-9140-x | Periodicals |
Keywords | Field | DocType |
Quantization,Finite frames,Random frames,Alternative duals,Compressed sensing | Discrete mathematics,Mathematical optimization,Mathematical analysis,Dual polyhedron,Matrix (mathematics),Sobolev space,Gaussian,Quantization (signal processing),Compressed sensing,Mathematics,Restricted isometry property,Bounded function | Journal |
Volume | Issue | ISSN |
13 | 1 | 1615-3375 |
Citations | PageRank | References |
21 | 0.86 | 16 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| C. Sinan Güntürk | 1 | 85 | 7.87 |
| Mark Lammers | 2 | 42 | 2.79 |
| Alexander M. Powell | 3 | 46 | 3.60 |
| Rayan Saab | 4 | 149 | 14.56 |
| Özgür Yilmaz | 5 | 685 | 51.36 |