# YALL1-Group: A solver for group/joint sparse reconstruction

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*'''A''': an m-by-n matrix with m < n, or a structure with the following fields: | *'''A''': an m-by-n matrix with m < n, or a structure with the following fields: | ||

- | : 1) A.times: a function handle for <math>A*x</math>; | + | : 1) A.times: a function handle for <math>A*x</math>; |

- | : 2) A.trans: a function handle for <math>A^T*x</math>; | + | : 2) A.trans: a function handle for <math>A^T*x</math>; |

- | : 3) A.invIpAAt: a function handle for <math>(\beta_1I_m+\beta_2AA^T)^{-1}*x</math>; | + | : 3) A.invIpAAt: a function handle for <math>(\beta_1I_m+\beta_2AA^T)^{-1}*x</math>; |

- | : 4) A.invAAt: a function handle for <math>(AA^T)^{-1}*x</math> | + | : 4) A.invAAt: a function handle for <math>(AA^T)^{-1}*x</math> |

## Revision as of 16:27, 12 June 2011

YALL1-Group is a MATLAB software package for group/joint sparse reconstruction, written by Wei Deng, Wotao Yin and Yin Zhang at Rice University.

## Model

(1) Group-sparse basis pursuit model:

Minimize subject to

where , , denotes the index set of the -th group, and is the weight for the -th group.

(2) Jointly-sparse basis pursuit model:

Minimize subject to

where , denotes the -th row of matrix , and is the weight for the -th row.

## Syntax

- [x,Out] = YALL1_group(A,b,groups,'param1',value1,'param2',value2,...);

## Input Arguments

**A**: an m-by-n matrix with m < n, or a structure with the following fields:

- 1) A.times: a function handle for ;
- 2) A.trans: a function handle for ;
- 3) A.invIpAAt: a function handle for ;
- 4) A.invAAt: a function handle for