Name
Abstract | ||
|---|---|---|
l1-minimization refers to finding the minimum l1-norm solution to an
underdetermined linear system b=Ax. It has recently received much attention,
mainly motivated by the new compressive sensing theory that shows that under
quite general conditions the minimum l1-norm solution is also the sparsest
solution to the system of linear equations. Although the underlying problem is
a linear program, conventional algorithms such as interior-point methods suffer
from poor scalability for large-scale real world problems. A number of
accelerated algorithms have been recently proposed that take advantage of the
special structure of the l1-minimization problem. In this paper, we provide a
comprehensive review of five representative approaches, namely, Gradient
Projection, Homotopy, Iterative Shrinkage-Thresholding, Proximal Gradient, and
Augmented Lagrange Multiplier. The work is intended to fill in a gap in the
existing literature to systematically benchmark the performance of these
algorithms using a consistent experimental setting. In particular, the paper
will focus on a recently proposed face recognition algorithm, where a sparse
representation framework has been used to recover human identities from facial
images that may be affected by illumination, occlusion, and facial disguise.
MATLAB implementations of the algorithms described in this paper have been made
publicly available. |
Year | Venue | DocType |
|---|---|---|
2010 | Computing Research Repository | Journal |
Volume | Citations | PageRank |
abs/1007.3 | 30 | 2.59 |
References | Authors | |
24 | 5 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Allen Y. Yang | 1 | 5216 | 183.98 |
| Arvind Ganesh | 2 | 4904 | 153.80 |
| Zihan Zhou | 3 | 833 | 39.42 |
| Shankar Sastry | 4 | 11977 | 1291.58 |
| Yi Ma | 5 | 14931 | 536.21 |