基于MATLAB的双树复小波变换（DTCWT）和双树复小波包变换（DTCWPT）的代码实现
一、双树复小波变换（DTCWT）实现
1. 核心函数代码
% 加载预置滤波器（需下载dtcwt_toolbox4_3工具箱）
load('qshift_b.mat'); % 包含qshift_b滤波器系数
load('near_sym_b.mat'); % 包含near_sym_b滤波器系数% 一维DTCWT分解
function [Yl, Yh] = dtcwt_1d(x, J, biort, qshift)if nargin < 3, biort = 'near_sym_b'; endif nargin < 4, qshift = 'qshift_b'; end[Yl, Yh] = dualtree(x, J, biort, qshift);
end% 二维DTCWT分解
function [Yl, Yh] = dtcwt_2d(x, J, biort, qshift)if nargin < 3, biort = 'near_sym_b'; endif nargin < 4, qshift = 'qshift_b'; end[Yl, Yh] = dtwavexfm2(x, J, biort, qshift);
end% 重构函数
function x = idtcwt_1d(Yl, Yh, biort, qshift)x = idualtree(Yl, Yh, biort, qshift);
endfunction x = idtcwt_2d(Yl, Yh, biort, qshift)x = dtwaveifm2(Yl, Yh, biort, qshift);
end
2. 示例应用代码
% 一维信号处理示例
t = 0:0.01:1;
x = sin(2*pi*5*t) + 0.5*randn(size(t)); % 含噪声信号
[J, ~] = wavedec(x, 3, 'db4'); % 多级分解% DTCWT分解
[Yl, Yh] = dtcwt_1d(x, 3, 'near_sym_b', 'qshift_b');% 重构验证
x_recon = idtcwt_1d(Yl, Yh, 'near_sym_b', 'qshift_b');
figure;
subplot(2,1,1); plot(t, x); title('原始信号');
subplot(2,1,2); plot(t, x_recon); title('重构信号');% 二维图像处理示例
load('lenna.mat'); % 加载标准测试图像
[X, map] = imread('lena.png');
X = im2double(X);% DTCWT分解
[Yl, Yh] = dtcwt_2d(X, 3, 'near_sym_b', 'qshift_b');% 低频子带可视化
figure; imshow(Yl(:,:,1), []); title('低频子带');
二、双树复小波包变换（DTCWPT）实现
1. 核心函数代码
% 双树复小波包分解
function [WPT] = dtwpt_2d(x, J, biort, qshift)[rows, cols] = size(x);WPT = cell(J, 6); % 6个高频子带% 初始分解[cA, cH, cV, cD] = dwt2(x, 'haar');WPT{1,1} = cA;for j = 1:J-1% 递归分解高频子带for k = 1:6subband = WPT{j,k};if ~isempty(subband)[cA, cH, cV, cD] = dwt2(subband, 'haar');WPT{j+1,2*k-1} = cA;WPT{j+1,2*k} = cH;endendend
end% 小波包重构
function x = idtwpt_2d(WPT, J, biort, qshift)% 从最低频子带开始重构current_band = WPT{J,1};for j = J-1:-1:1% 合并相邻子带for k = 1:6if ~isempty(WPT{j,2*k-1}) && ~isempty(WPT{j,2*k})% 使用逆DWT重构coeffs = [WPT{j,2*k-1}; WPT{j,2*k}];current_band = idwt2(coeffs(:,1), coeffs(:,2), 'haar');endendendx = current_band;
end
2. 示例应用代码
% 图像小波包分解
[X, map] = imread('lena.png');
X = im2double(X);
[WPT] = dtwpt_2d(X, 3, 'near_sym_b', 'qshift_b');% 显示各层分解结果
figure;
for j = 1:3subplot(3,6,j*2-1); imshow(WPT{j,1}, []); title(sprintf('Level %d Low', j));subplot(3,6,j*2); imshow(WPT{j,2}, []); title(sprintf('Level %d High', j));
end% 重构验证
X_recon = idtwpt_2d(WPT, 3, 'near_sym_b', 'qshift_b');
figure; imshow(X_recon); title('重构图像');
三、应用案例
1. 图像去噪（DTCWT）
% 添加高斯噪声
noisy_img = imnoise(X, 'gaussian', 0, 0.01);% DTCWT分解
[Yl, Yh] = dtcwt_2d(noisy_img, 3, 'near_sym_b', 'qshift_b');% 阈值处理
for j = 1:3Yh{j} = wthresh(Yh{j}, 's', 0.1*max(abs(Yh{j}(:))));
end% 重构
denoised_img = dtwaveifm2(Yl, Yh, 'near_sym_b', 'qshift_b');
2. 机械故障诊断（DTCWPT）
% 加载振动信号
load('vibration_signal.mat');% 小波包分解
[WPT] = dtwpt_2d(signal, 4, 'near_sym_b', 'qshift_b');% 特征提取
energy = zeros(4,6);
for j = 1:4for k = 1:6energy(j,k) = sum(WPT{j,k}.^2);end
end% 分类决策
if max(energy(:,4)) > thresholddiagnosis = '轴承外圈故障';
elsediagnosis = '正常状态';
end
参考代码 双树复小波变换和双树复小波包变换代码 www.youwenfan.com/contentcnl/81077.html
该方案结合经典理论与工程实践，适用于信号处理、图像分析等领域。建议根据具体应用场景调整分解层数和滤波器参数。
