# ASP

December 2012

## Description

ASP is a set of Matlab routines for solving several variations of the sparse optimization problem

\[ \underset{x}{\text{minimize}}\ \ \lambda \Vert x \Vert_1 + \frac12 \Vert Ax - b\Vert_2^2 \]

It implements algorithms for the following:

- basis pursuit denoising (including \(Ax=b\))
- orthogonal matching pursuit
- homotopy version of basis pursuit denoising
- reweighted basis pursuit for approximating 0-norm solutions
- sequential compressed sensing (adding rows to \(A\) and \(b\))
- nonnegative least-squares
- sparse-residual and sparse-solution regression
- generalized Lasso for sparsity in \(Bx\)

## References

- M. P. Friedlander and M. A. Saunders (2012). A dual active-set quadratic programming method for finding sparse least-squares solutions, Technical Report, Dept of Computer Science, University of British Columbia, July 30, 2012.
- Hatef Monajemi, Sina Jafarpour, Matan Gavish, Stat 330/CME 362 Collaboration and David L. Donoho (2012). Deterministic matrices matching the compressed sensing phase transitions of Gaussian random matrices, PNAS 110:4, 1181-1186. [This paper made use of ASP (via BPdual) as well as CVX, FISTA, SPGL1, and Mosek.]

## Download

Version 1.0, December 17, 2012