Name
Title | ||
|---|---|---|
Signal recovery method for compressive sensing using relaxation and second-order cone programming |
Abstract | ||
|---|---|---|
A signal recovery method for compressive sensing under noisy measurements is proposed. The problem is formulated as a nonconvex nonsmooth constrained optimization problem that uses the smoothly clipped absolute deviation (SCAD) function to promote sparsity. Relaxation is employed by means of a series of local linear approximations (LLAs) of the SCAD in a constrained formulation. The relaxation is shown to converge to a minimum of the original nonconvex constrained optimization problem. In order to solve each nonsmooth convex relaxation problem, a second-order cone programming (SOCP) formulation is used, which can be applied by using standard state-of-the-art SOCP solvers such as SeDuMi. Experimental results demonstrate that signals recovered using the proposed method exhibit reduced ℓ∞ reconstruction error when compared with competing methods such as ℓ1 -Magic. Simulations demonstrate that significant reduction in the reconstruction error can be achieved with computational cost that is comparable to that required by the ℓ1 -Magic algorithm. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1109/ISCAS.2011.5938018 | Circuits and Systems |
Keywords | Field | DocType |
approximation theory,concave programming,signal reconstruction,£1-Magic algorithm,LLA,SCAD function,SOCP formulation,compressive sensing,local linear approximation,noisy measurement,nonconvex nonsmooth constrained optimization problem,nonsmooth convex relaxation problem,reconstruction error,second-order cone programming formulation,signal recovery method,smoothly clipped absolute deviation function,Compressive sensing,second-order-cone programming,signal recovery,smoothly clipped absolute deviation | Linear approximation,Second-order cone programming,Mathematical optimization,Noise measurement,Control theory,Algorithm,Approximation theory,Convex function,Lagrangian relaxation,Signal reconstruction,Compressed sensing,Mathematics | Conference |
ISSN | ISBN | Citations |
0271-4302 E-ISBN : 978-1-4244-9472-9 | 978-1-4244-9472-9 | 1 |
PageRank | References | Authors |
0.35 | 1 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Flávio C. A. Teixeira | 1 | 2 | 0.99 |
| Stuart W. A. Bergen | 2 | 2 | 1.33 |
| A. Antoniou | 3 | 267 | 30.79 |