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

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(Model)
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subject to <math>Ax=b,</math>
subject to <math>Ax=b,</math>
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where <math>A\in \mathbb{R}^{m\times n}\,(m<n)</math>, <math>b\in \mathbb{R}^m</math>, <math>g_i</math> is 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.
+
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> is 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.
+
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 15:33, 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     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<n), 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<n),\, B\in \mathbb{R}^{m\times l}, 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,varargin);

Input Description

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