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iCAPs/packages/gspbox/utils/gsp_norm_l2_filterbank.m
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gsp_norm_l2_filterbank.m
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function n = gsp_norm_l2_filterbank(G, W, x, param)
%GSP_NORM_L2_FILTERBANK Compute the l2 norm of the analysis coefficients
% Usage: n = gsp_norm_l2_filterbank(G, W, x);
%
% Input parameters:
% G : Graph structure
% W : Filterbank (cell array of functions)
% x : coefficients
% param: structure of optional paramter
% Output parameters:
% n : L2 norm
%
% GSP_NORM_L2_FILTERBANK(G, W, x, param) computes:
%
% n = || A W^* x -y ||_2^2
%
% param is a Matlab structure containing the following fields:
%
% param.A : Forward operator (default: Id).
%
% param.y : measurements (default: 0).
%
%
% Url: http://lts2research.epfl.ch/gsp/doc/utils/gsp_norm_l2_filterbank.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: 26 March 2014
if ~isfield(G,'lmax')
G = gsp_estimate_lmax(G);
warning(['GSP_NORM_L1_FILTERBANK: To be more efficient you should run: ',...
'G = gsp_estimate_lmax(G); before using this proximal operator.']);
end
if nargin < 4, param=struct; end
if ~isfield(param, 'y'), param.nu = 0; end
if ~isfield(param, 'A'), param.A = @(x) x; end
n = norm(param.A(gsp_filter_synthesis(G,W,x))-param.y,'fro')^2;
end
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