1 简介
作为一种信号预处理手段,信号去噪在众多信号处理应用中发挥着重要的作用.到目前为止,信号去噪问题被大量研究,并取得了许多重要成果,涌现出了包括非局部均值(NLM)去噪算法在内的一批优秀的去噪方法.值得一提的是,相比于传统的局部去噪算法,非局部均值去噪算法有着更好的去噪性能和更好的信号细节保留能力.
2 部分代码
function [denoisedSig,debug] = NLM_1dDarbon(signal,lambda,P,PatchHW)
% function [denoisedSig,debug] = NLM_1dDarbon(signal,lambda,P,PatchHW)
% Implements fast NLM method of Darbon et al, for a 1-D signal
% INPUTS:
% signal: input signal (vector)
% lambda: Gaussian scale factor
% P: max search distance
% PatchWH: patch half-width
% OUTPUTS:
% denoisedSig: the NLM-denoised signal
% debug: structure containing various quantitities that can help debug
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% =========================================================================
% PAPER INFO:
% Brian Tracey and Eric Miller, "Nonlocal means denoising of ECG signals",
% IEEE Transactions on Biomedical Engineering, Vol 59, No 9, Sept
% 2012, pages 2383-2386
% -------------------------------------------------------------------------
% PLEASE CITE THIS PAPER, IF YOU USE THIS CODE FOR ACADEMIC PURPOSES
% -------------------------------------------------------------------------
% For all inquiries, please contact author Brian Tracey(btracey[at]alum.mit.edu)
%
% Last Update 05/09/2013
% =========================================================================
%
if length(P)==1, % scalar has been entered; expand into patch sample index vector
Pvec = -P:P;
else
Pvec = P; % use the vector that has been input
end
debug=[];
N = length(signal);
denoisedSig = NaN*ones(size(signal));
% to simpify, don't bother denoising edges
iStart=1+PatchHW+1;
iEnd = N-PatchHW;
denoisedSig(iStart:iEnd) = 0;
debug.iStart = iStart;
debug.iEnd = iEnd;
% initialize weight normalization
Z = zeros(size(signal));
cnt = zeros(size(signal));
% convert lambda value to 'h', denominator, as in original Buades papers
Npatch = 2*PatchHW+1;
h = 2*Npatch*lambda^2;
for idx = Pvec % loop over all possible differences: s-t
% do summation over p - Eq. 3 in Darbon
k=1:N;
kplus = k+idx;
igood = find(kplus>0 & kplus<=N); % ignore OOB data; we could also handle it
SSD=zeros(size(k));
SSD(igood) = (signal(k(igood))-signal(kplus(igood))).^2;
Sdx = cumsum(SSD);
for ii=iStart:iEnd % loop over all points 's'
distance = Sdx(ii+PatchHW) - Sdx(ii-PatchHW-1); % Eq 4; this is in place of point-by-point MSE
% but note the -1; we want to icnlude the point ii-iPatchHW
w = exp(-distance/h); %Eq 2 in Darbon
t = ii+idx; % in the papers, this is not made explicit
if t>1 && t<=N
denoisedSig(ii) = denoisedSig(ii) + w*signal(t);
Z(ii) = Z(ii) + w;
cnt(ii) = cnt(ii)+1;
end
end
end % loop over shifts
% now apply normalization
denoisedSig = denoisedSig./(Z+eps);
debug.Z = Z;
return
3 仿真结果
4 参考文献
[1]蔡斌. 非局部均值去噪算法研究[D]. 中国科学技术大学, 2015.
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