Revision 3dc3b6f146d45d55e0d2c215ce3c24a7c7014fac authored by Michael Friedlander on 06 January 2012, 06:40:54 UTC, committed by Michael Friedlander on 06 January 2012, 06:40:54 UTC
1 parent 8392c22
spg_group.m
function [x,r,g,info] = spg_group( A, b, groups, sigma, options )
%SPG_GROUP Solve jointly-sparse basis pursuit denoise (BPDN)
%
% SPG_GROUP is designed to solve the basis pursuit denoise problem
%
% (BPDN) minimize sum_k ||X_{i : GROUPS(i) = k}||_2
% subject to ||A X - B||_2,2 <= SIGMA,
%
% where A is an M-by-N matrix, B is a vector, GROUPS is vector
% containing the group number of the corresponding index in X, and
% SIGMA is a nonnegative scalar. In all cases below, A can be an
% explicit M-by-N matrix or matrix-like object for which the
% operations A*x and A'*y are defined (i.e., matrix-vector
% multiplication with A and its adjoint.)
%
% Also, A can be a function handle that points to a function with the
% signature
%
% v = A(w,mode) which returns v = A *w if mode == 1;
% v = A'*w if mode == 2.
%
% X = SPG_GROUP(A,B,G,SIGMA) solves the BPDN problem. If SIGMA=0,
% SIGMA=[] or SIGMA is omitted, then the jointly-sparse basis
% pursuit (BP) problem is solved; i.e., the constraints in the BPDN
% problem are taken as AX=B.
%
% X = SPG_GROUP(A,B,G,SIGMA,OPTIONS) specifies options that are set
% using SPGSETPARMS.
%
% [X,R,G,INFO] = SPG_GROUP(A,B,GROUPS,SIGMA,OPTIONS) additionally
% returns the residual R = B - A*X, the objective gradient G = A'*R,
% and an INFO structure. (See SPGL1 for a description of this last
% output argument.)
%
% See also spgl1, spgSetParms, spg_bp, spg_lasso.
% Thanks to Aswin Sankaranarayanan for pointing out performance
% issues with an earlier version of the group preprocessing code.
% Copyright 2008, Ewout van den Berg and Michael P. Friedlander
% http://www.cs.ubc.ca/labs/scl/spgl1
% $Id$
if ~exist('options','var'), options = []; end
if ~exist('sigma','var') || isempty(sigma), sigma = 0; end
if ~exist('groups','var') || isempty(groups)
error('Third argument cannot be empty.');
end
if ~exist('b','var') || isempty(b)
error('Second argument cannot be empty.');
end
if ~exist('A','var') || isempty(A)
error('First argument cannot be empty.');
end
% Preprocess the groups, normalize numbering
g = groups(:);
n = length(g);
[gidx,idx1,idx2] = unique(g);
groups = sparse(idx2,1:n,ones(1,n),length(gidx),n);
% Set projection specific functions
options.project = @(x,weight,tau) NormGroupL2_project(groups,x,weight,tau);
options.primal_norm = @(x,weight ) NormGroupL2_primal(groups,x,weight);
options.dual_norm = @(x,weight ) NormGroupL2_dual(groups,x,weight);
tau = 0;
x0 = [];
[x,r,g,info] = spgl1(A,b,tau,sigma,x0,options);
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