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

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== Optional Input Arguments ==
== Optional Input Arguments ==
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*''''StopTolerance'''': stopping tolerance value.
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*''''GrpWeights'''': weights for the groups
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| ''''StopTolerance'''' || positive scalar || stopping tolerance value
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| ''''GrpWeights'''' || Example || weights for the groups
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Revision as of 16:09, 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.


Contents

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,'param1',value1,'param2',value2,...);

Required Input Arguments

  • A: an m-by-n matrix with m < n, or a structure with the following fields:
1) A.times(required): a function handle for LaTeX: A*x;
2) A.trans(required): a function handle for LaTeX: A^T*x;
3) A.invIpAAt: a function handle for LaTeX: (\beta_1I_m+\beta_2AA^T)^{-1}*x;
4) A.invAAt: a function handle for LaTeX: (AA^T)^{-1}*x.

Note: A.invIpAAt is only required when (a) primal solver is to be used, and b) A is non-orthonormal, and (c) exact linear system solving is to be performed.

     A.invAAt is only required when (a) dual solver is to be used, and b) A is non-orthonormal, and (c) exact linear system solving is to be performed.
  • b: an m-vector for the group-sparse model or an m-by-l matrix for the joint-sparse model.
  • groups: an n-vector containing the group number of the corresponding component of LaTeX: x for the group-sparse model, or [] for the joint-sparse model.

Optional Input Arguments

Parameter Names Value Description
'StopTolerance' positive scalar stopping tolerance value
'GrpWeights' Example weights for the groups
Example Example Example
Example Example Example
Example Example Example
Example Example Example
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