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iCAPs_v2/packages/gspbox/operators/gsp_pyramid_synthesis.m
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gsp_pyramid_synthesis.m
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function [reconstruction,coarse_approximations]=gsp_pyramid_synthesis(Gs,coarsest_approximation,prediction_errors,param)
%GSP_PYRAMID_SYNTHESIS Synthesizes a signal from its graph pyramid transform coefficients
% Usage: reconstruction=gsp_pyramid_synthesis(Gs,coarsest_approximation,prediction_errors);
% reconstruction=gsp_pyramid_synthesis(Gs,coarsest_approximation,prediction_errors,param);
%
% Input parameters:
% Gs : A multiresolution sequence of graph structures, including the idx parameters tracking the subsampling pattern.
% coarsest_approximation : The coarsest approximation of the original signal.
% prediction_errors : Cell array with the prediction errors at each level.
% Output parameters:
% reconstruction : The synthesized signal.
% coarse_approximations : Sequence of coarse approximations
%
% 'gsp_pyramid_synthesis(Gs,coarsest_approximation,prediction_errors)'
% synthesizes a signal from its graph pyramid transform coefficients.
%
% param is a structure containing optional arguments including
%
% param.regularize_epsilon : Interpolation parameter.
% param.least_squares : Set to 1 to use the least squares synthesis
% (default=0)
% param.use_landweber : Set to 1 to use the Landweber iteration
% approximation in the least squares synthesis.
% param.landweber_its : Number of iterations in the Landweber
% approximation for least squares synthesis.
% param.landweber_tau : Parameter for the Landweber iteration.
% param.h_filters : A cell array of graph spectral filters. If just
% one filter is included, it is used at every level of the pyramid.
% These filters are required for least squares synthesis, but not for
% the direct synthesis method
% Default
%
% h(x) = 0.5 / ( 0.5 + x)
%
% Please read the documentation of GSP_FILTER_ANALYSIS for other
% optional arguments.
%
% See also: gsp_graph_multiresolution gsp_pyramid_analysis
% gsp_pyramid_analysis_single gsp_pyramid_cell2coeff
% gsp_pyramid_synthesis_single
%
% Demo: gsp_demo_pyramid
%
% References:
% D. I. Shuman, M. J. Faraji, and P. Vandergheynst. A framework for
% multiscale transforms on graphs. arXiv preprint arXiv:1308.4942, 2013.
%
%
%
% Url: http://lts2research.epfl.ch/gsp/doc/operators/gsp_pyramid_synthesis.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 : David I Shuman, Nathanael Perraudin.
% Date : 26 November 2015
% Testing: test_pyramid
% Read input parameters
if nargin<4
param=struct;
end
if ~isfield(param, 'least_squares') param.least_squares=0; end
num_levels=length(prediction_errors);
if param.least_squares
if ~isfield(param, 'h_filters')
error('h-filter not provided');
end
end
if ~isfield(param,'h_filters')
param.h_filters=cell(num_levels,1);
for i=1:num_levels
param.h_filters{i}=@(x) .5./(.5+x);
end
elseif length(param.h_filters)==1
if iscell(param.h_filters)
filter=param.h_filters{1};
else
filter=param.h_filters;
end
param.h_filters=cell(num_levels,1);
for i=1:num_levels
param.h_filters{i}=filter;
end
elseif length(param.h_filters)~=num_levels
error('param.h_filters should be a cell array of length 1 or num_levels');
end
% Compute the inverse pyramid transform
coarse_approximations = cell(num_levels+1,1);
coarse_approximations{num_levels+1} = coarsest_approximation;
for i=num_levels:-1:1
param.h_filter=param.h_filters{i};
coarse_approximations{i}=gsp_pyramid_synthesis_single(Gs{i},coarse_approximations{i+1},prediction_errors{i},Gs{i+1}.mr.idx,param);
end
reconstruction=coarse_approximations{1};
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