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function [xo]=elitistthresh(xi,lambda,varargin)
%-*- texinfo -*-
%@deftypefn {Function} elitistthresh
%@verbatim
%ELITISTTHRESH elitist (hard/soft) thresholding
% Usage: xo=elitistthresh(xi,lambda);
%
% ELITISTTHRESH(xi,lambda) performs hard elitist thresholding on xi,
% with threshold lambda. The input xi must be a two-dimensional array,
% the first dimension labelling groups, and the second one labelling
% members. All coefficients within a given group are shrunk according to
% the value of the l^1 norm of the group in comparison to the threshold
% value lambda.
%
% ELITISTTHRESH(x,lambda,'soft') will do the same using soft
% thresholding.
%
% ELITISTTHRESH accepts the following flags at the end of the line of input
% arguments:
%
% 'hard' Perform hard thresholding. This is the default.
%
% 'soft' Perform soft thresholding.
%
% 'full' Return the output as a full matrix. This is the default.
%
% 'sparse' Return the output as a sparse matrix.
%
%
%
% References:
% M. Kowalski. Sparse regression using mixed norms. Appl. Comput. Harmon.
% Anal., 27(3):303--324, 2009.
%
% M. Kowalski and B. Torresani. Sparsity and persistence: mixed norms
% provide simple signal models with dependent coefficients. Signal, Image
% and Video Processing, 3(3):251--264, 2009.
%
%@end verbatim
%@strong{Url}: @url{http://ltfat.github.io/doc/sigproc/elitistthresh.html}
%@seealso{groupthresh, demo_audioshrink}
%@end deftypefn
% Copyright (C) 2005-2016 Peter L. Soendergaard <peter@sonderport.dk>.
% This file is part of LTFAT version 2.3.1
%
% 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/>.
% AUTHOR : Bruno Torresani.
if nargin<2
error('Too few input parameters.');
end;
if (prod(size(lambda))~=1 || ~isnumeric(lambda))
error('lambda must be a scalar.');
end;
% Define initial value for flags and key/value pairs.
definput.flags.iofun={'hard','soft'};
definput.flags.outclass={'full','sparse'};
[flags,keyvals]=ltfatarghelper({},definput,varargin,mfilename);
NbGroups = size(xi,1);
NbMembers = size(xi,2);
if flags.do_sparse
xo = sparse(size(xi));
else
xo = zeros(size(xi));
end;
for g=1:NbGroups,
y = sort(abs(xi(g,:)),'descend');
rhs = cumsum(y);
rhs = rhs .* lambda ./ (1 + lambda * (1:NbMembers));
M_g = find(diff(sign(y-rhs)));
if (M_g~=0)
tau_g = lambda * norm(y(1:M_g),1)/(1+lambda*M_g);
else
tau_g = 0;
end
xo(g,:) = thresh(xi(g,:),tau_g,flags.iofun,flags.outclass);
end
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