bat1.m

编程实现基于小波变换尺度相关性去噪算法

function bat1
%非正交的二次样条二进小波
h = [0 0 0.125 0.375 0.375 0.125 0 0].*sqrt(2);
g = [0 0 0 -1 1 0 0 0].*sqrt(2);
g1 = [0 0.015625 0.109375 0.34375 -0.34375 -0.109375 -0.015625 0].*sqrt(2);

%正交的二次样条二进小波
% h = [0 0 0 0 0.375 0.125 0.373].*sqrt(2);
% g = [0 0 0 0 0.5798 0.0869 0.0061].*sqrt(2);
%g1 = [0 0.015625 0.109375 0.34375 -0.34375 -0.109375 -0.015625 0].*sqrt(2);

%正交的三次样条二进小波
% h = [0 0.0625 0.2500 0.3750 0.2500 0.0625 0].*sqrt(2);
% g = [-0.00008 -0.01643 -0.10872 -0.59261 0 0.59261 0.10872 0.01643 0.00008].*sqrt(2);
%g1 = [0 0.015625 0.109375 0.34375 -0.34375 -0.109375 -0.015625 0].*sqrt(2);


l = 512;
x = [1:l];

% s0 = sin(2*pi*x/l*4).*sin(2*pi*x/l*8).*sin(2*pi*x/l)*10;
% s = s0+rand(1,l)*2;
% s = sin(2*pi*x/l*2);

s(1:l/4) = 2;
s(l/4+1:l*1/2) = 5;
s(l*1/2+1:l*3/4) = 3;
s(l*3/4+1:l) = 4;

% s(1:l/4) = [1:l/4]./20 + l/8/20;
% s(l/4+1:l*1/2) = s(l/4:-1:1);
% s(l/2+1:l) = s(1:l/2);


n = 7;
[a d] = swt1d_decomp(s,n,h,g);

% figure,title('原始信号')
% plot(s);
% [Y I] = max(s);
% I
figure, title('逼近矩阵');
for i=1:n
    subplot(n,1,i);
    title(['逼近矩阵 ' num2str(i)]);
    plot(a(:,i));
    set(gca,'XTick',0:50:l);
%     [Y I] = max(a(:,i));
%     I
end
saveas(gcf,['pic' filesep 'a'],'png'),close(gcf);

figure, title('细节信息矩阵');
for i=1:n
    subplot(n,1,i);
    title(['细节矩阵 ' num2str(i)]);
    plot(d(:,i));
    set(gca,'XTick',0:50:l);
end
saveas(gcf,['pic' filesep 'd'],'png'),close(gcf);


% 重构
s1 = swt1d_recon(a,d,n,h,g1);

ss = s1(:,[2:n+1]);
row = ceil(sqrt(n));
col = ceil(n/row);

figure, title('重构矩阵');
for i=1:n
    subplot(n,1,i);
    title(['重构矩阵' num2str(n-i+1)]);
    plot(ss(:,n-i+1));
    set(gca,'XTick',0:50:l);
%         [Y I] = max(ss(:,n-i+1));
%         I
end
saveas(gcf,['pic' filesep 'reconst'],'png'),close(gcf);

sr = ss(:,n);
figure
subplot(3,1,1), hold on, title('原始信号'),plot(s), set(gca,'XTick',0:50:l);
subplot(3,1,2), hold on, title('重构信号'),plot(sr), set(gca,'XTick',0:50:l);
subplot(3,1,3), hold on, title('误差信号'),plot(sr-s'),
set(gca,'XTick',0:50:l);
saveas(gcf,['pic' filesep 'result'],'png'),close(gcf);

%     [Y I] = max(sr);
%     I

% figure;
% for i=1:n
%     subplot(n,1,i);
%     title(['重构矩阵误差' num2str(n-i+1)]);
%     sr = ss(:,n-i+1);
%     so = a(:,i);
%     plot(sr-so);
%     set(gca,'XTick',1:10:l);
% end