Homec4science
Diffusion iCAPs public version 2 (master) Browse

iCAPs_v2/packages/gspbox/stationarity/gsp_wiener_inpainting.m
e5f5005bb2efmaster

Last Change
Raw File

gsp_wiener_inpainting.m
View Options

function [sol, infos] = gsp_wiener_inpainting(G,y, M, psd, psd_noise, param)
%GSP_WIENER_INPAINTING Solve wiener in-painting problem
% Usage: sol = gsp_wiener_inpainting(G,y, M, psd, psd_noise)
% sol = gsp_wiener_inpainting(G,y, M, psd, psd_noise, param)
% [sol, infos] = gsp_wiener_inpainting(...)
%
% Input parameters:
% G : Graph (GSP structure)
% y : Measurements (column vector)
% M : Mask (vector)
% psd : PSD filter (anonymous function)
% psd_noise : PSD filter of the noise or single number
% param : Optional optimization parameters
% Output parameters:
% sol : Solution
% infos : Convergence informations
%
% This function solves the following wiener optimization problem:
%
% argmin_x || M x - y ||_2^2 + || w(L) x ||_2^2
%
% Please refer to the reference for more information about this problem.
% This function requires the UNLocBox to work.
%
% Please refer to the function gsp_filter_analysis and solvep to know how
% param can be set.
%
% References:
% N. Perraudin and P. Vandergheynst. Stationary signal processing on
% graphs. arXiv preprint arXiv:1601.02522, 2016.
%
%
%
% Url: http://lts2research.epfl.ch/gsp/doc/stationarity/gsp_wiener_inpainting.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: 6 January 2016
if nargin<6
param = struct;
end
Mop =@(x) bsxfun(@times,M,x);
if isnumeric(psd_noise) && sum(abs(psd_noise))==0
ffid.eval = @(x) eps;
ffid.prox = @(x,T) x-Mop(x)+Mop(y);
wl = @(x) 1./(psd(x)+eps);
fprox = @(T) @(x) psd(x)./(2*T + psd(x) + eps);
else
ffid.grad = @(x) 2*Mop(Mop(x)-y);
ffid.eval = @(x) norm(Mop(x)-y,'fro')^2;
ffid.beta = 2;
if isnumeric(psd_noise)
wl = @(x) psd_noise./(psd(x)+eps);
fprox = @(T) @(x) psd(x)./(psd(x)+2*T*psd_noise + eps);
else
wl = @(x) psd_noise(x)./(psd(x)+eps);
fprox = @(T) @(x) psd(x)./(psd(x)+2*T*psd_noise(x) + eps);
end
end
fprior.prox = @(x,T) gsp_filter_analysis(G,fprox(T),x, param);
fprior.eval = @(x) 0.5*norm(gsp_filter_analysis(G,wl,x,param),'fro')^2;
[sol, infos] = solvep(y,{ffid,fprior},param);
% [sol, infos] = gsp_wiener_optimization(G, y, ffid, psd, psd_noise, param);
end
c4science · Help