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

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*'''b''': an m-vector for the group-sparse model or an m-by-l matrix for the joint-sparse model. | *'''b''': an m-vector for the group-sparse model or an m-by-l matrix for the joint-sparse model. | ||

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+ | *'''groups''': an n-vector containing the group number of the corresponding component of <math>x</math> for the group-sparse model, or [] for the joint-sparse model. |

## Revision as of 16:44, 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(required): a function handle for ;
- 2) A.trans(required): a function handle for ;
- 3) A.invIpAAt: a function handle for ;
- 4) A.invAAt: a function handle for .

Note: A.invIpAAt is only required when (a) primal solver is to be used, and b) A is non-orthonormal, and (c) exact linear system solving is to be performed.

A.invAAt is only required when (a) dual solver is to be used, and b) A is non-orthonormal, and (c) exact linear system solving is to be performed.

**b**: an m-vector for the group-sparse model or an m-by-l matrix for the joint-sparse model.

**groups**: an n-vector containing the group number of the corresponding component of for the group-sparse model, or [] for the joint-sparse model.