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基于小波分析和TV非凸模型的图像去模糊去噪算法

news 2025/10/2 9:22:23

一、算法框架设计

graph TDA[输入图像] --> B[小波分解]B --> C{多尺度处理}C --> D[高频子带TV优化]C --> E[低频子带非局部处理]D --> F[小波重构]E --> FF --> G[后处理]

二、核心算法实现

1. 小波分解模块

% 使用db4小波进行4层分解
[c,l] = wavedec2(I,4,'db4');
[cA,cH,cV,cD] = detcoef2('all',c,l);

2. TV非凸模型构建

% 定义TV正则化项
tv_term = @(u) sum(sqrt(sum(gradient(u).^2,3)));% 非局部相似性权重计算
W = compute_nonlocal_weights(I,patch_size);% 构建优化问题
min_u { ||I - H*u||^2 + λ*(tv_term(u) + β*sum(W.*|u - I|^2)) };

3. 多尺度处理流程

for each scale% 高频子带处理high_band = cH(:,:,k);denoised_high = tv_denoise(high_band, lambda);% 低频子带处理low_band = cA(:,:,k);denoised_low = nonlocal_tv(denoised_low, W);% 更新小波系数cH(:,:,k) = denoised_high;cA(:,:,k) = denoised_low;
end

三、关键技术创新

1. 自适应TV参数选择

% 基于局部梯度统计的参数调整
local_gradient = stdfilt(gradient(I), true(3));
lambda = 0.1 * median(local_gradient(:));

2. 非局部相似块搜索

function W = compute_nonlocal_weights(I, patch_size)[m,n] = size(I);W = zeros(m,n);for i = 1:mfor j = 1:nref_patch = imcrop(I, [j-2,j+2,i-2,i+2]);candidates = im2col(I, [5,5], 'distinct');distances = sum((candidates - ref_patch).^2, 2);[~,idx] = sort(distances);W(i,j) = sum(exp(-idx(1:20)./50));endend
end

3. 混合优化算法

% ADMM迭代优化
u = initialization(I);
for iter = 1:max_iter% x-updatex = prox_l1(u + z, tau);% z-updatez_old = z;z = soft_threshold(x - u, lambda/tau);% u-updateu = u + x - z;% 收敛判断if norm(x - z) < 1e-4break;end
end