cyclespinning.m

平移不变法用于消除图像变换产生的为吉布斯效应

clear;
clc;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  1.原始信号

f=50;    % 信号频率
fs=800;  % 采样频率
N=128;   % 采样点 

%  信号赋值
n=1:N;
y=sin(2*pi*f*n/fs);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  2.噪声
noise=0.4*rand(1,128);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  3.染噪信号
y_noise=y+noise;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  4.硬消噪采用cycle_spinning技术

%  累加量
z5=zeros(1,N);

%  平移变换频移法
for i=1:N;
    z=circshift(y_noise.',i-1).';  %  源信号右平移
    [z1,z2]=lwt(z,'db3');    %  小波正变换
    z2=zeros(1,N/2);         %  高频分量全部为零（主要噪声，硬消噪）
    z3=ilwt(z1,z2,'db3');    %  小波反变换  
    z4=circshift(z3.',-(i-1)).';  %  变换后信号左平移  
    z5=z5+z4/N;  %  平均  
end;
    
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%  5.显示

error=norm(y-z5)/norm(y);  % 相对误差

figure(1);
subplot(2,1,1)
plot(y,'r');
legend('源信号');
subplot(2,1,2);
plot(y_noise);
legend('染噪信号');


figure(2);
subplot(2,1,1)
plot(y,'r');
legend('源信号');
title(error);
subplot(2,1,2);
plot(z5);
legend('消噪后信号');