Matlab| sparse auxiliary signal denoising and pattern recognition in time series data

Catalog

One 、 summary

Two 、 Example and simulation

Example 1 ：

Example 2 ：

Example 3 ：

Example 4 ：

Example 5 ：

Example 6 ：

3、 ... and 、Matlab Code implementation

 

One 、 summary

In this paper, by combining linear time invariant filter 、 Orthogonal multiresolution representation and method based on sparsity , It solves the problems of signal de-noising and pattern recognition when processing batch mode time series data . Spectrum transformation expressed by state space of digital filter , Low pass the high-order zero phase 、 A new method for designing high pass and bandpass infinite impulse response filters as matrices . A technique based on near end gradient is also proposed , It is used to factorize a special class of zero phase high pass and band-pass digital filters , So that the factorization product preserves the zero phase property of the filter , The input sparse derivative component is added to the signal model . In order to show the application of the novel filter design , Verify and propose a new signal model , To simultaneously denoise and identify patterns of interest . First, we use our proposed filter design to test the existing signal model , The model combines linear time invariant （LTI） Filters and methods based on sparsity . The filter design proposed in this paper is combined with the existing signal model , A method called sparse auxiliary signal denoising is developed （SASD） A new signal model . Using simulation data , Proved SASD Robustness of the signal model under different order filters and noise levels . thereafter , A new method called sparsity aided pattern recognition is proposed and derived （SAPR） A new signal model . stay SAPR in , Will also LTI Bandpass filter and sparse based method with orthogonal multiresolution representation （ Such as wavelet ） Combination , To detect a specific mode in the input signal . Last , This paper combines signal denoising with pattern recognition , A method called sparse auxiliary signal denoising and pattern recognition is derived （SASDPR） A new signal model . Sleep EEG data were used to detect K Complexes and sleep spindles , So that explains SAPR and SASDPR Functions of the framework .

Two 、 Example and simulation

Example 1 ：

Sparse auxiliary signal denoising ( SASD ) The algorithm combines total variation denoising and low-pass filtering to filter the noisy signal , Thus, the signal discontinuity is maintained .

              

Example 2 ：

Use the banded matrix to demonstrate an example of zero phase filtering ：

           

Example 3 ：

Sparse auxiliary signal denoising ( SASD ) The algorithm combines total variation denoising and low-pass filtering to filter the noisy signal , Thus, the signal discontinuity is maintained . In this case , We use LPF、TVD、SASS and SASD Denoise ECG signal ：

          

Example 4 ：

Sparse auxiliary signal denoising and pattern recognition (SASDPR) The oscillation mode of interest in a given signal will be de noised and detected simultaneously ：

           

Example 5 ：

Sparse auxiliary signal denoising and pattern recognition (SASDPR) The oscillation mode of interest in a given signal will be de noised and detected simultaneously ：

             

Example 6 ：

Sparse aided pattern recognition (SAPR) The wavelet pattern in the detection signal ：

        

3、 ... and 、Matlab Code implementation

This article only shows part of the code , All code points here ： We are shipping your work details

function [y, f, s, x, w] = generate_signal( fs, sigma )

%%  Initialize noise level and signal length 
rng('default')
N = 10*fs;
n = 0:N-1;

%%  Produce low-frequency synthetic ingredients 
f = 0.1;
f = sin(2*f/fs*pi*n);      

%%  Oscillate 
s = zeros(size(n));
o = 13;
s(200+(1:fs)) = sin(2*pi*o/fs*(1:fs)) .* hamming(fs)';

%%  Sparse piecewise constant 
x = zeros(size(n));
x(100:110) = -1;
x(400:420) = 1;

%%  Add noise 
w = sigma*randn(size(n));
y = f+s+x+w;

end

 

%% plot_signals( y, x_ex3, kc, k, tk, th, binX, binA, method)
%
% Inputs:
%   y       -  Noise signal 
%   x_ex3   -  Sleep spindle signal 
%   k       -  detected k- Synthetic wave signal 
%   tk      - Teager-Kaiser Energy operators 
%   th      -  Spindle detection threshold 
%   binX    -  Binary vector 
%   binA    -  Binary vector with algorithm annotation spindle 
%   method  - SASDPR/DETOKS
%
% Outputs:
%   None

%% ________________________________________________________________________
%%
function plot_signals( y, x_ex3, kc, k, tk, th, binX, binA, method)

global simdata;
fs = simdata.fs;

if strcmp(method, 'DETOKS')
    txt_1 = [method, ', EEG signal ($\mathbf{y}$), ','$\lambda_1$ = ', num2str(simdata.lam0_detoks), ...
        ', $\lambda_2$ = ', num2str(simdata.lam1_detoks), ', $\lambda_3$ = ', num2str(simdata.lam2_detoks),...
        ', $\mu$ = ', num2str(simdata.mu_detoks)];
    txt_2 = [method, ', Low-frequency signal'];
    txt_3 = [method, ', Teager-Kaiser energy operator, Threshold = ', num2str(simdata.th_detoks)];
    txt_4 = [method, ', Detected EEG K-complexes'];
elseif strcmp(method, 'SAPR')
    txt_1 = [method, ', EEG signal ($\mathbf{y}$), ','$\lambda_1$ = ', num2str(simdata.lam0_sapr), ...
        ', $\lambda_2$ = ', num2str(simdata.lam1_sapr), ', $\eta$ = ', num2str(simdata.eta_sapr),...
        ', $\mu$ = ', num2str(simdata.mu_sapr)];
    txt_2 = [method, ', K-Complex signal ($\mathbf{x}_2$)'];
    txt_3 = [method, ', Teager-Kaiser energy operator, Threshold = ', num2str(simdata.th_sapr)];
    txt_4 = [method, ', Detected EEG K-complexes'];
end

N = length(y);
n = 0:N-1;

%% Plot
figure('rend','painters','pos',[100 100 550 500]);
clf

subplot(4,1,1);
text(-0.1,0.98,'(a)','Units', 'Normalized', 'VerticalAlignment', 'Top'); hold on;
plot(n/fs, y, 'k'); hold on;
p0 = plot(n/fs, x_ex3, 'r'); hold off;
title(txt_1,'interpreter','latex')
legend([p0], {'K-complex'},'location','north');
legend boxoff;
set(gca, 'box', 'off')
axis tight;

subplot(4,1,2);
text(-0.1,0.98,'(b)','Units', 'Normalized', 'VerticalAlignment', 'Top'); hold on;
p0 = plot(n/fs, kc, 'k'); hold on;
p1 = plot(n/fs, k, '--k'); hold off;
title(txt_2,'interpreter','latex')
if strcmp(method, 'SAPR')
    legend([p1,p0], {'$\mathbf{\Psi} \mathbf{k}$', ...
        '$\mathbf{B}^T \mathbf{B} \mathbf{\Psi} \mathbf{k}$'},'interpreter','latex', ...
        'location','north');
    legend boxoff;
end
set(gca, 'box', 'off')
axis tight;

subplot(4,1,3);
text(-0.1,0.98,'(c)','Units', 'Normalized', 'VerticalAlignment', 'Top'); hold on;
p0 = plot(n/fs, tk); hold on;
p1 = plot(n/fs, th*ones(1,N), 'r--'); hold off;
title(txt_3,'interpreter','latex')
legend([p0,p1], {'TKEO','Threshold'},'location','north');
legend boxoff;
set(gca, 'box', 'off')
axis tight;

subplot(4,1,4);
text(-0.1,0.98,'(d)','Units', 'Normalized', 'VerticalAlignment', 'Top'); hold on;
plot(n/fs, binX, 'Color', [0,0,0]+0.7,'linewidth',1.0); hold on;
plot(n/fs, binA, 'k');
title(txt_4,'interpreter','latex')
xlabel('Time (seconds)','interpreter','latex')
legend('Expert',method,'location','north');
legend boxoff
set(gca, 'box', 'off')
ylim([-0.2, 1.2])

printme_pdf = @(ex,meth) print('-dpdf', sprintf('../../results/%s_%s',ex,meth));
printme_pdf('ex6',lower(method));

% printme_eps = @(ex,meth) print('-depsc', sprintf('figures/%s_%s',ex,meth));
% printme_eps('ex6',lower(method));


end

Program ： 

 

 

data ：