基于改进高斯-拉普拉斯滤波器的一维时间序列平滑与降噪（MATLAB）

以图像处理为例，拉普拉斯算子是基于图像的二阶导数来找到边缘并搜索过零点，传统的拉普拉斯算子常产生双像素宽的边缘，对于较暗区域中的亮斑进行边缘检测时，拉普拉斯运算就会使其变得更亮。因此，与梯度算子一样，拉普拉斯算子不能抑制图像的噪声。如果有一种算子能够将高斯平滑滤波器与拉普拉斯算子结合起来，在进行边缘检测之前先平滑掉噪声，一定能够取得良好的效果，因此，高斯—拉普拉斯算子被提出。鉴于此，采用一种改进的高斯-拉普拉斯滤波器对一维时间序列进行平滑与降噪，运行环境为MATLAB R2018，测试了地震信号，微震信号。

clc
clear 
close all
%load Input example
load mport1-1.txt
x=mport1_1';
% Sigma and Filter Order 
% Tune sigma, and N according to the application you want to use.
sigma = 0.5;
N = 10;
% For More Scaling dividing by sigma.
[Gaussian_1D_2_Diff_Modified]=IGLF(sigma,N) /sigma;
% Filtering The Input (Denoising the Input Signal)
Output = filter (Gaussian_1D_2_Diff_Modified,1,x);
% Output Squaring 
Output = Output.^2;
% For more smoothing, average movabale window is obatined for m samples
% with k stride (moving by k samples)
% Adjustce m, and k according to the application you want to use.
Output_More_Smoothing = zeros(1,size(x,2));
m = 8;
k = 1;
count = 1;
 for j=1:k:(length(Output))-max([m k])
 Output_More_Smoothing(count)=(mean(Output(j:j+m-1)));
 count = count +1;
 end
 
% Plotting 
% Plotting the Cofficients of MLOG.
figure(1)
plot( (1:N), Gaussian_1D_2_Diff_Modified, 'LineWidth',3)
xlabel('Index (n)','FontSize',14,'FontWeight','bold')
ylabel('MLOG Mask Values','FontSize',14,'FontWeight','bold')
title('MLOG MASK','FontSize',14,'FontWeight','bold')
set(gca,'fontsize',12,'FontWeight','bold')
% Plotting Input, Output of MLOG, and Smoothed Output Signal.
figure(2)
subplot(3,1,1),plot(1:length(x),x)
xlabel('Sample Index','FontSize',14,'FontWeight','bold')
ylabel('Count','FontSize',14,'FontWeight','bold')
title('Input Signal','FontSize',14,'FontWeight','bold')
set(gca,'fontsize',12,'FontWeight','bold')
subplot(3,1,2),plot(1:length(Output), Output)
xlabel('Sample Index','FontSize',14,'FontWeight','bold')
ylabel('Count^2','FontSize',14,'FontWeight','bold')
title('Output Signal of IGLF Filter','FontSize',14,'FontWeight','bold')
set(gca,'fontsize',12,'FontWeight','bold')
subplot(3,1,3),plot(1:length(Output_More_Smoothing), Output_More_Smoothing)
xlabel('Sample Index','FontSize',14,'FontWeight','bold')
ylabel('Count^2','FontSize',14,'FontWeight','bold')
title('Smoothed Output Signal','FontSize',14,'FontWeight','bold')
set(gca,'fontsize',12,'FontWeight','bold')


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