# Category:Misc Solvers

### From SparseSolver

These solvers do not fit into other categories, or else they are waiting to be categorized.

## Contents |

### IHT

The simplest algorithm is iterative hard-thresholding (IHT)^{[1]} which directly tries to solve the best subset selection problem. It has been analyzed and can provide some recovery guarantees. Thomas Blumensath has a collection of greedy and hard thresholding algorithms (GreedLab and HardLab).

ALPS is an accelerated variant of IHT, and CLASH is a variant that also includes l1 norm constraints and has some provable recovery guarantees.

### Smoothing l0 quasi-norm

The SL0 method attempts to smooth the l0 quasi-norm and thus approximately solve the best subset selection problem.

### Coordinate Descent

A coordinate descent algorithm for l1 functions is proposed in ^{[2]}

### Special Applications

#### MRI

- sparseMRI by Michael Lustig and Stanford co-authors. For MRI.
- l1-spirit by Michael Lustig. This is custom for MRI reconstruction, and is very well-done code (MATLAB, which calls mex files and can call CUDA executables to take advantage of a fast graphics card).

## Uncategorized

- KF-CS: Kalman Filtered CS (and other sequential CS algorithms)
- k-t FOCUSS. FOCUSS is a type of iteratively-reweighted least-squares (IRLS).
- Cycling matching pursuit (CMP)] with code. They say it's similar to OMP

## References

- ↑ T. Blumensath, M. E. Davies,
*Iterative hard thresholding for compressed sensing*,**Harm. Anal.**27 (2009), no. 3, 265--274. arXiv:0805.0510 - ↑ J. Friedman, T. Hastie, and R. Tibshirani,
*Regularization paths for generalized linear models via coordinate descent*,**J. Stat. Software**33 (2010), no. 1.

## Pages in category "Misc Solvers"

The following 4 pages are in this category, out of 4 total.