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

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 Revision as of 16:17, 12 June 2011 (edit) (→Input Description)← Previous diff Revision as of 16:21, 12 June 2011 (edit) (undo) (→Input Arguments)Next diff → Line 27: Line 27: *'''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 $A*x$ 1) A.times: a function handle for $A*x$ - 2) A.trans: a function handle for [itex]A_T*x[itex] + 2) A.trans: a function handle for [itex]A^T*x + 3) A.invIpAAt: a function handle for [itex](\beta_1I_m+\beta_2AA^T)^{-1}*x

## Revision as of 16:21, 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 $LaTeX: A^T*x$
3) A.invIpAAt: a function handle for $LaTeX: (\beta_1I_m+\beta_2AA^T)^{-1}*x$