NLM Local Polynomial Regression (NLM-LPR)

Simple example on Swoosh


We present here the following methods for Local Polynomial Regression (LPR) in the case of
-Linear Filter (LF)
-Yaroslavksy's filter (YF)
-Non-Local Means (NLM)
-Non-Local Means-Average (NLMA)
-Membership oracle (MO)

The kernel used is the box kernel. See also DEMO_NLMLPR.m and README.TXT in the associate zip file for more details.

Authors: \( \textbf{E. Arias-Castro} \), \(\textbf{J. Salmon} \) and \(\textbf{R. Willett} \)

Copyright (C) 2011 NLM-LPR project See The GNU Public License (GPL)

Initialization

close all
clear all
addpath('tools');
addpath('functions');

Build the true and noisy images

sigma=50;
ima = mean(double(imread('data/swoosh.png')),3);
ima_nse = ima + sigma * randn(size(ima));

Parameters initialization

param.patch_width=7;
param.search_width=15;

param.h_NLM=3.5*param.patch_width*param.patch_width*sigma^2;
%param.h_OYF=900;%
%param.h_YF=10*(sigma)^2;%
%param.h_NLMA=4*sigma^2/(param.patch_width)^2;

Compute the NLM-LPR estimations for \(r=0,1,2\)

tic
ima_fil_NLM0=NLM0(ima_nse,param.h_NLM,param.search_width,param.patch_width);
ima_fil_NLM1=NLM1(ima_nse,param.h_NLM,param.search_width,param.patch_width);
ima_fil_NLM2=NLM2(ima_nse,param.h_NLM,param.search_width,param.patch_width);

% Other methods:
% LF         :  ima_fil_LF0=LF0(ima_nse,param.search_width);
% YF         :  ima_fil_YF0=YF1(ima_nse,param.h_YF,param.search_width);
% NLMA       :  ima_fil_NLMA0=NLM2(ima_nse,param.h_NLMA,param.search_width,param.patch_width);
% Oracle YF  :  ima_fil_OYF0=OYF2(ima,ima_nse,param.h_OYF,param.search_width);

Total time

toc
Elapsed time is 379.851588 seconds.

Display result

figure('Position',[100 100  700 700])

subplot(2,2,1)
plotimage(ima_nse);
title('Noisy');
set(get(gca,'Title'),'FontSize',16);
subplot(2,2,2);
plotimage(ima_fil_NLM0);
title('Estimate with NLM and r=0');
set(get(gca,'Title'),'FontSize',16);
subplot(2,2,3);
plotimage(ima_fil_NLM1);
title('Estimate with NLM and r=1');
set(get(gca,'Title'),'FontSize',16);
subplot(2,2,4);
plotimage(ima_fil_NLM2);
title('Estimate with NLM and r=2');
set(get(gca,'Title'),'FontSize',16);

linkaxes

"Oracle inequalities and minimax rates for non-local means and related adaptive kernel-based methods"
E. , J. Salmon, R. , SIAM J. Imaging Sci., vol.5, pp. 944--992, 2012, PDF.

Corresponding Matlab toolbox ZIP.

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