gsp_design_meyer.m
2cb18aae5832master

gsp_design_meyer.m
View Options

			function [ g,t ] = gsp_design_meyer(G, Nf, param)
			%GSP_DESIGN_MEYER Design the meyer filterbank
			% Usage: g = gsp_design_meyer(G, Nf, param);
			% gsp_design_meyer(G ,Nf);
			% gsp_design_meyer(G);
			%
			% Input parameters:
			% G : Graph or upper bound on the Laplacian spectrum
			% Nf : Number of filters to cover the interval [0,lmax] (default 6)
			% param : Structure of optional parameters
			% Output parameters:
			% g : A cell array of filters
			%
			% This function return a array of filters designed to be meyer wavelet.
			%
			% param is an optional structure containing the following fields
			%
			% param.t*: vector of scale to be used (default: log scale)
			% param.verbose*: verbosity level. 0 no log - 1 display warnings.
			% (default 1)
			%
			% This function will compute the maximum eigenvalue of the laplacian. To
			% be more efficient, you can precompute it using:
			%
			% G = gsp_estimate_lmax(G);
			%
			% Example:
			%
			% Nf = 4;
			% G = gsp_sensor(100);
			% G = gsp_estimate_lmax(G);
			% g = gsp_design_meyer(G, Nf);
			% gsp_plot_filter(G,g);
			%
			% This function is inspired by the sgwt_toolbox.
			%
			% See also:
			%
			% Url: http://lts2research.epfl.ch/gsp/doc/filters/gsp_design_meyer.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, David K. Hammond
			% Date: 18 March 2014



			if nargin < 3
			param = struct;
			end

			if ~isfield(param,'verbose'), param.verbose = 1; end

			if isstruct(G)
			if ~isfield(G,'lmax')
			if param.verbose
			fprintf('GSP_DESIGN_MEYER has to compute lmax \n')
			end
			G = gsp_estimate_lmax(G);
			end
			lmax = G.lmax;
			else
			lmax = G;
			end

			if ~isfield(param,'t')
			param.t = (4/(3lmax)) 2.^(Nf-2:-1:0);
			end


			if param.verbose
			if length(param.t) ~= Nf - 1
			warning(['GSP_KERNEL_MEYER: You have specified ',...
			'more scales than Number of filter -1']);
			end
			end

			t = param.t;
			g = cell(Nf,1);

			g{1}= @(x) kernel_meyer(t(1)*x,'sf');
			for j=1:Nf-1
			g{j+1}= @(x) kernel_meyer(t(j)*x,'wavelet');
			end



			end




			function r=kernel_meyer(x,kerneltype)
			% sgwt_kernel_meyer : evaluates meyer wavelet kernel and scaling function
			% function r=sgwt_kernel_meyer(x,kerneltype)
			%
			% Inputs
			% x : array of independent variable values
			% kerneltype : string, either 'sf' or 'wavelet'
			%
			% Ouputs
			% r : array of function values, same size as x.
			%
			% meyer wavelet kernel : supported on [2/3,8/3]
			% meyer scaling function kernel : supported on [0,4/3]
			%
			% Use of this kernel for SGWT proposed by Nora Leonardi and Dimitri Van De Ville,
			% "Wavelet Frames on Graphs Defined by fMRI Functional Connectivity"
			% International Symposium on Biomedical Imaging, 2011
			l1=2/3;
			l2=4/3;%2*l1;
			l3=8/3;%4*l1;
			v=@(x) x.^4.(35-84x+70x.^2-20x.^3) ;

			% as we initialize r with zero, computed function will implicitly be zero for
			% all x not in one of the three regions defined above
			r=zeros(size(x));
			switch kerneltype
			case 'sf'
			r(x<l1)=1;
			r(x>=l1 & x<l2)=cos((pi/2)*v(abs(x(x>=l1 & x<l2))/l1-1));
			case 'wavelet'
			r(x>=l1 & x<l2)=sin((pi/2)*v(abs(x(x>=l1 & x<l2))/l1-1));
			r(x>=l2 & x<l3)=cos((pi/2)*v(abs(x(x>=l2 & x<l3))/l2-1));
			otherwise
			error(sprintf('unknown kernel type %s',kerneltype));
			end


			end

iCAPs/packages/gspbox/filters/gsp_design_meyer.m2cb18aae5832master

gsp_design_meyer.mView Options

iCAPs/packages/gspbox/filters/gsp_design_meyer.m
2cb18aae5832master

gsp_design_meyer.m
View Options