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iCAPs_v2/packages/gspbox/operators/gsp_pyramid_analysis_single.m
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gsp_pyramid_analysis_single.m
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function [coarse_approximation,prediction_error]=gsp_pyramid_analysis_single(G,signal,keep_inds,h_filter,param)
%GSP_PYRAMID_ANALYSIS_SINGLE Compute a single level of the graph pyramid transform coefficients
% Usage: [coarse_approximation,prediction_error]=gsp_pyramid_analysis_single(G,signal,keep_inds,h_filter,param);
%
% Input parameters:
% signal : Graph signal to analyze.
% G : Graph structure on which the signal resides.
% keep_inds : The indices of the vertices to keep when downsampling the graph and signal.
% h_filter : The H filter in the pyramid transform.
% Output parameters:
% coarse_approximation : The next coarse approximation.
% prediction_error : The next prediction error.
%
% 'gsp_pyramid_analysis_single(G,signal,keep_inds,h_filter,param)' computes
% a single level of the graph pyramid transform coefficients.
%
% param is a structure containing optional arguments including
% param.regularize_epsilon : Interpolation parameter.
%
% Please read the documentation of GSP_FILTER_ANALYSIS for other
% optional arguments.
%
% See also: gsp_graph_multiresolution gsp_pyramid_analysis
% gsp_pyramid_synthesis gsp_pyramid_cell2coeff
%
% 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_analysis_single.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
% Compute the next coarse approximation and prediction error
h_filtered_signal = gsp_filter(G, h_filter, signal, param);
coarse_approximation = h_filtered_signal(keep_inds, :);
prediction = gsp_interpolate(G, coarse_approximation, keep_inds, param);
prediction_error = signal - prediction;
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