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iCAPs/packages/gspbox/prox/gsp_solve_l0.m
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gsp_solve_l0.m
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function [alpha, info] = gsp_solve_l0(G, W, s, lambda, param )
%GSP_SOLVE_L0 Solve a BP problem using l0
% Usage: alpha = gsp_solve_l0(G, W, s, lambda );
% alpha = gsp_solve_l0(G, W, s, lambda, param );
%
% Input parameters:
% G : Graph
% W : Filterbank
% s : Signal
% lambda : regularization parameter
% param : Optional structure of parameters
% Ouptut parameters:
% alpha : Filterbank coefficients
%
% This function solve the following minimization problem
%
% argmin_alpha lambda || alpha ||_0 + || W'alpha - s ||_2^2
%
% argmin_\alpha \lambda \| \alpha \|_0 + \| W' \alpha - s \|_2^2
%
% In param, you can optionaly set:
%
% param.verbose : 0 no log, 1 a summary at convergence, 2 print main
% steps (default: 1)
%
% info is a Matlab structure containing optimization information from
% the UNLocBoX
%
%
% Url: http://lts2research.epfl.ch/gsp/doc/prox/gsp_solve_l0.php
% Copyright (C) 2013-2016 Nathanael Perraudin, Johan Paratte, David I Shuman.
% This file is part of GSPbox version 0.7.0
%
% This program is free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see <http://www.gnu.org/licenses/>.
% If you use this toolbox please kindly cite
% N. Perraudin, J. Paratte, D. Shuman, V. Kalofolias, P. Vandergheynst,
% and D. K. Hammond. GSPBOX: A toolbox for signal processing on graphs.
% ArXiv e-prints, Aug. 2014.
% http://arxiv.org/abs/1408.5781
% Author: Nathanael Perraudin
% Date : 8 February 2015
% Testing : test_gsp_solve_l0
if nargin < 5
param = struct;
end
if ~isfield(param,'verbose'), param.verbose = 1; end
Nf = length(W);
Ns = size(s,2);
% L0 minimization
paraml0.verbose = param.verbose -1;
fl0.prox = @(x,T) prox_l0(x,lambda * T,paraml0);
fl0.eval = @(x) lambda *sum(sum(abs(x)>0));
A = @(x) gsp_filter_synthesis(G,W,x,param);
At = @(x) gsp_filter_analysis(G,W,x,param);
[~, bound] = gsp_filterbank_bounds(G,W);
ffid.grad = @(x) 2* At(A(x)-s);
ffid.eval = @(x) norm(A(x)-s,'fro')^2;
ffid.beta = 2*bound;
% Starting point
if ~isfield(param,'guess'), param.guess = zeros(G.N*Nf,Ns); end
% Solver
paramsolver = param;
[alpha, info] = forward_backward(param.guess,fl0,ffid,paramsolver);
end
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