YALL1-Group: A solver for group/joint sparse reconstruction
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:[x,Out] = YALL1_group(A,b,groups,'param1',value1,'param2',value2,...); | :[x,Out] = YALL1_group(A,b,groups,'param1',value1,'param2',value2,...); | ||
- | == Input Arguments == | + | == Required Input Arguments == |
*'''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: | ||
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*'''groups''': an n-vector containing the group number of the corresponding component of <math>x</math> for the group-sparse model, or [] for the joint-sparse model. | *'''groups''': an n-vector containing the group number of the corresponding component of <math>x</math> for the group-sparse model, or [] for the joint-sparse model. | ||
+ | |||
+ | == Required Input Arguments == | ||
+ | |||
+ | ''''StopTolerance'''': stopping tolerance value. |
Revision as of 16:49, 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:
Minimizesubject to
![]()
where ,
,
denotes the index set of the
-th group, and
is the weight for the
-th group.
(2) Jointly-sparse basis pursuit model:
Minimizesubject to
![]()
where ,
denotes the
-th row of matrix
, and
is the weight for the
-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
;
- 2) A.trans(required): a function handle for
;
- 3) A.invIpAAt: a function handle for
;
- 4) A.invAAt: a function handle for
.
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
for the group-sparse model, or [] for the joint-sparse model.
Required Input Arguments
'StopTolerance': stopping tolerance value.