基于MATLAB的双树复小波变换和双树复小波包变换的代码实现

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

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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'; end
    if 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'; end
    if 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);
end

function 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');

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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 = 1:6
            subband = 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;
            end
        end
    end
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 = 1:6
            if ~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');
            end
        end
    end
    x = 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 = 1:3
    subplot(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');

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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 = 1:3
    Yh{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 = 1:4
    for k = 1:6
        energy(j,k) = sum(WPT{j,k}.^2);
    end
end

% 分类决策
if max(energy(:,4)) > threshold
    diagnosis = '轴承外圈故障';
else
    diagnosis = '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。