Name
Abstract | ||
|---|---|---|
The convergence rate is analyzed for the sparse reconstruction by separable approximation (SpaRSA) algorithm for minimizing a sum $f(\mathbf{x})+\psi(\mathbf{x})$, where $f$ is smooth and $\psi$ is convex, but possibly nonsmooth. It is shown that if $f$ is convex, then the error in the objective function at iteration $k$ is bounded by $a/k$ for some $a$ independent of $k$. Moreover, if the objective function is strongly convex, then the convergence is $R$-linear. An improved version of the algorithm based on a cyclic version of the BB iteration and an adaptive line search is given. The performance of the algorithm is investigated using applications in the areas of signal processing and image reconstruction. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1137/090775063 | SIAM J. Imaging Sciences |
Keywords | Field | DocType |
nonmonotone convergence,bb iteration,sparsa,linear convergence,sparse recovery,nonsmooth optimization,cyclic version,adaptive line search,objective function,improved version,gradient-based methods,signal processing,sublinear convergence,sparse reconstruction,compressed sensing,denoising,bb method,ista,separable approximation,convergence rate,image reconstruction,line search | Convergence (routing),Mathematical optimization,Mathematical analysis,Separable space,Regular polygon,Convex function,Line search,Rate of convergence,Mathematics,Compressed sensing,Bounded function | Journal |
Volume | Issue | ISSN |
4 | 1 | 1936-4954 |
Citations | PageRank | References |
13 | 0.77 | 14 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| William W. Hager | 1 | 1603 | 214.67 |
| Dzung T. Phan | 2 | 61 | 10.32 |
| Hongchao Zhang | 3 | 809 | 43.29 |