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

(Difference between revisions)
 Revision as of 14:34, 12 June 2011 (edit) (→Syntax)← Previous diff Revision as of 15:17, 12 June 2011 (edit) (undo) (→Input Description)Next diff → Line 23: Line 23: :[x,Out] = YALL1_group(A,b,groups,'param1',value1,'param2',value2,...); :[x,Out] = YALL1_group(A,b,groups,'param1',value1,'param2',value2,...); - == Input Description == + == 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 $A*x$ + 2) A.trans: a function handle for [itex]A_T*x[itex]

## Revision as of 15:17, 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,...);

## 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 $LaTeX: A*x$
2) A.trans: a function handle for $LaTeX: A_T*x[itex]$