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

(Difference between revisions)
 Revision as of 15:33, 12 June 2011 (edit) (→Model)← Previous diff Revision as of 15:34, 12 June 2011 (edit) (undo) (→Syntax)Next diff → Line 21: Line 21: == Syntax == == Syntax == - :[x,Out] = YALL1_group(A,b,groups,varargin); + :[x,Out] = YALL1_group(A,b,groups,'param1',value1,'param2',value2,...); == Input Description == == Input Description ==

## Revision as of 15:34, 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 $LaTeX: \|x\|_{w,2,1}:=\sum_{i=1}^s w_i\|x_{g_i}\|_2,$

subject to $LaTeX: Ax=b,$


where $LaTeX: A\in \mathbb{R}^{m\times n}\,(m, $LaTeX: b\in \mathbb{R}^m$, $LaTeX: g_i$ denotes the index set of the $LaTeX: i$-th group, and $LaTeX: w_i\geq0$ is the weight for the $LaTeX: i$-th group.

(2) Jointly-sparse basis pursuit model:

                  Minimize $LaTeX: \|X\|_{w,2,1}:=\sum_{i=1}^n w_i\|x^i\|_2,$
subject to $LaTeX: AX=B,$


where $LaTeX: A\in \mathbb{R}^{m\times n}\,(m, $LaTeX: x^i$ denotes the $LaTeX: i$-th row of matrix $LaTeX: X$, and $LaTeX: w_i\geq0$ is the weight for the $LaTeX: i$-th row.

## Syntax

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