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

### From Wikimization

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subject to <math>Ax=b,</math> | subject to <math>Ax=b,</math> | ||

- | where <math>A\in \mathbb{R}^{m\times n}\,(m<n)</math>, <math>b\in \mathbb{R}^m</math>, <math>g_i</math> | + | where <math>A\in \mathbb{R}^{m\times n}\,(m<n)</math>, <math>b\in \mathbb{R}^m</math>, <math>g_i</math> denotes the index set of the <math>i</math>-th group, and <math>w_i\geq0</math> is the weight for the <math>i</math>-th group. |

(2) Jointly-sparse basis pursuit model: | (2) Jointly-sparse basis pursuit model: | ||

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subject to <math>AX=B,</math> | subject to <math>AX=B,</math> | ||

- | where <math>A\in \mathbb{R}^{m\times n}\,(m<n),\, B\in \mathbb{R}^{m\times l}</math>, <math>x^i</math> | + | where <math>A\in \mathbb{R}^{m\times n}\,(m<n),\, B\in \mathbb{R}^{m\times l}</math>, <math>x^i</math> denotes the <math>i</math>-th row of matrix <math>X</math>, and <math>w_i\geq0</math> is the weight for the <math>i</math>-th row. |

== Syntax == | == Syntax == |

## Revision as of 14:33, 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,varargin);