基于最小拉普拉斯残差插值的去马赛克算法

基于最小拉普拉斯残差插值的去马赛克算法。这是一种用于从Bayer模式图像中恢复全彩色图像的高质量算法。

算法原理

最小拉普拉斯残差插值(MLRI)基于以下关键思想：

• 颜色通道间的相关性：在同一位置，不同颜色通道间存在强相关性
• 拉普拉斯算子：用于估计插值方向的平滑性
• 残差最小化：选择使拉普拉斯残差最小的插值方向

MATLAB实现

function [rgb_image] = mlri_demosaic(bayer_image, pattern)
% 最小拉普拉斯残差插值去马赛克算法
% 输入：
%   bayer_image - Bayer模式原始图像
%   pattern - Bayer模式类型 ('rggb', 'bggr', 'grbg', 'gbrg')
% 输出：
%   rgb_image - 恢复的全彩色图像

    if nargin < 2
        pattern = 'rggb'; % 默认RGGB模式
    end
    
    [h, w] = size(bayer_image);
    rgb_image = zeros(h, w, 3);
    
    % 根据Bayer模式提取各通道采样位置
    [R, G, B] = extract_bayer_channels(bayer_image, pattern);
    
    % 步骤1: 绿色通道插值（使用MLRI）
    G_interp = mlri_green_interpolation(bayer_image, pattern, R, G, B);
    
    % 步骤2: 红色和蓝色通道插值
    R_interp = mlri_redblue_interpolation(bayer_image, pattern, G_interp, 'red');
    B_interp = mlri_redblue_interpolation(bayer_image, pattern, G_interp, 'blue');
    
    % 组合最终图像
    rgb_image(:, :, 1) = R_interp;
    rgb_image(:, :, 2) = G_interp;
    rgb_image(:, :, 3) = B_interp;
    
    % 后处理
    rgb_image = min(max(rgb_image, 0), 1);
end

function [R, G, B] = extract_bayer_channels(bayer, pattern)
% 从Bayer图像中提取各通道的采样位置
    [h, w] = size(bayer);
    R = zeros(h, w);
    G = zeros(h, w);
    B = zeros(h, w);
    
    switch lower(pattern)
        case 'rggb'
            % R G
            % G B
            R(1:2:end, 1:2:end) = bayer(1:2:end, 1:2:end);
            G(1:2:end, 2:2:end) = bayer(1:2:end, 2:2:end);
            G(2:2:end, 1:2:end) = bayer(2:2:end, 1:2:end);
            B(2:2:end, 2:2:end) = bayer(2:2:end, 2:2:end);
            
        case 'bggr'
            % B G
            % G R
            B(1:2:end, 1:2:end) = bayer(1:2:end, 1:2:end);
            G(1:2:end, 2:2:end) = bayer(1:2:end, 2:2:end);
            G(2:2:end, 1:2:end) = bayer(2:2:end, 1:2:end);
            R(2:2:end, 2:2:end) = bayer(2:2:end, 2:2:end);
            
        case 'grbg'
            % G R
            % B G
            G(1:2:end, 1:2:end) = bayer(1:2:end, 1:2:end);
            R(1:2:end, 2:2:end) = bayer(1:2:end, 2:2:end);
            B(2:2:end, 1:2:end) = bayer(2:2:end, 1:2:end);
            G(2:2:end, 2:2:end) = bayer(2:2:end, 2:2:end);
            
        case 'gbrg'
            % G B
            % R G
            G(1:2:end, 1:2:end) = bayer(1:2:end, 1:2:end);
            B(1:2:end, 2:2:end) = bayer(1:2:end, 2:2:end);
            R(2:2:end, 1:2:end) = bayer(2:2:end, 1:2:end);
            G(2:2:end, 2:2:end) = bayer(2:2:end, 2:2:end);
    end
end

function G_interp = mlri_green_interpolation(bayer, pattern, R, G, B)
% 基于MLRI的绿色通道插值
    [h, w] = size(bayer);
    G_interp = G; % 初始化，已有G像素保持不变
    
    % 定义拉普拉斯核
    laplacian_kernel = [0, 1, 0; 1, -4, 1; 0, 1, 0];
    
    % 根据模式确定插值位置
    switch lower(pattern)
        case 'rggb'
            % 在R和B位置插值G
            for i = 2:h-1
                for j = 2:w-1
                    if mod(i,2) == 1 && mod(j,2) == 1 % R位置
                        G_interp(i,j) = interpolate_g_at_r(bayer, i, j, laplacian_kernel, pattern);
                    elseif mod(i,2) == 0 && mod(j,2) == 0 % B位置
                        G_interp(i,j) = interpolate_g_at_b(bayer, i, j, laplacian_kernel, pattern);
                    end
                end
            end
            
        case 'bggr'
            % 类似处理其他模式...
    end
    
    % 边界处理
    G_interp = handle_boundaries(G_interp);
end

function g_value = interpolate_g_at_r(bayer, i, j, laplacian_kernel, pattern)
% 在R位置插值G通道
    % 水平方向插值候选
    g_horizontal = (bayer(i, j-1) + bayer(i, j+1)) / 2;
    
    % 垂直方向插值候选
    g_vertical = (bayer(i-1, j) + bayer(i+1, j)) / 2;
    
    % 计算拉普拉斯残差
    residual_h = compute_laplacian_residual(bayer, i, j, g_horizontal, laplacian_kernel, 'horizontal', pattern);
    residual_v = compute_laplacian_residual(bayer, i, j, g_vertical, laplacian_kernel, 'vertical', pattern);
    
    % 选择最小残差的方向
    if abs(residual_h) < abs(residual_v)
        g_value = g_horizontal;
    elseif abs(residual_v) < abs(residual_h)
        g_value = g_vertical;
    else
        g_value = (g_horizontal + g_vertical) / 2;
    end
end

function g_value = interpolate_g_at_b(bayer, i, j, laplacian_kernel, pattern)
% 在B位置插值G通道
    % 与R位置类似，但考虑Bayer模式差异
    g_horizontal = (bayer(i, j-1) + bayer(i, j+1)) / 2;
    g_vertical = (bayer(i-1, j) + bayer(i+1, j)) / 2;
    
    residual_h = compute_laplacian_residual(bayer, i, j, g_horizontal, laplacian_kernel, 'horizontal', pattern);
    residual_v = compute_laplacian_residual(bayer, i, j, g_vertical, laplacian_kernel, 'vertical', pattern);
    
    if abs(residual_h) < abs(residual_v)
        g_value = g_horizontal;
    elseif abs(residual_v) < abs(residual_h)
        g_value = g_vertical;
    else
        g_value = (g_horizontal + g_vertical) / 2;
    end
end

function residual = compute_laplacian_residual(bayer, i, j, g_candidate, laplacian_kernel, direction, pattern)
% 计算拉普拉斯残差
    [h, w] = size(bayer);
    residual = 0;
    
    % 3x3邻域
    neighborhood = zeros(3,3);
    
    for di = -1:1
        for dj = -1:1
            ni = i + di;
            nj = j + dj;
            if ni >= 1 && ni <= h && nj >= 1 && nj <= w
                neighborhood(di+2, dj+2) = bayer(ni, nj);
            end
        end
    end
    
    % 计算当前拉普拉斯值
    current_laplacian = sum(sum(neighborhood .* laplacian_kernel));
    
    % 创建候选邻域
    candidate_neighborhood = neighborhood;
    candidate_neighborhood(2,2) = g_candidate; % 中心位置使用候选值
    
    % 计算候选拉普拉斯值
    candidate_laplacian = sum(sum(candidate_neighborhood .* laplacian_kernel));
    
    % 残差为两者之差
    residual = candidate_laplacian - current_laplacian;
end

function channel_interp = mlri_redblue_interpolation(bayer, pattern, G_interp, channel)
% 基于MLRI的红色/蓝色通道插值
    [h, w] = size(bayer);
    
    switch lower(channel)
        case 'red'
            base_channel = 'r';
        case 'blue'
            base_channel = 'b';
    end
    
    [R, G, B] = extract_bayer_channels(bayer, pattern);
    
    if strcmpi(channel, 'red')
        channel_data = R;
    else
        channel_data = B;
    end
    
    channel_interp = channel_data;
    laplacian_kernel = [0, 1, 0; 1, -4, 1; 0, 1, 0];
    
    % 在缺失位置插值
    for i = 3:h-2
        for j = 3:w-2
            if channel_interp(i,j) == 0 % 需要插值的位置
                % 使用颜色差值的恒常性假设
                if strcmpi(channel, 'red')
                    channel_interp(i,j) = interpolate_redblue_at_position(bayer, G_interp, i, j, laplacian_kernel, pattern, 'red');
                else
                    channel_interp(i,j) = interpolate_redblue_at_position(bayer, G_interp, i, j, laplacian_kernel, pattern, 'blue');
                end
            end
        end
    end
    
    channel_interp = handle_boundaries(channel_interp);
end

function value = interpolate_redblue_at_position(bayer, G_interp, i, j, laplacian_kernel, pattern, channel)
% 在特定位置插值红色或蓝色通道
    % 四个对角线方向候选
    candidates = zeros(1,4);
    residuals = zeros(1,4);
    
    % 对角线位置
    positions = [-1,-1; -1,1; 1,-1; 1,1];
    
    for k = 1:4
        di = positions(k,1);
        dj = positions(k,2);
        
        % 获取相邻的同通道像素
        if strcmpi(channel, 'red')
            neighbor_val = get_red_value(bayer, pattern, i+di, j+dj);
        else
            neighbor_val = get_blue_value(bayer, pattern, i+di, j+dj);
        end
        
        % 计算颜色差值
        g_center = G_interp(i, j);
        g_neighbor = G_interp(i+di, j+dj);
        
        % 候选值基于颜色差值恒常性
        candidates(k) = neighbor_val + (g_center - g_neighbor);
        
        % 计算残差
        residuals(k) = compute_color_difference_laplacian(bayer, G_interp, i, j, candidates(k), laplacian_kernel, channel, pattern);
    end
    
    % 选择最小残差的候选
    [~, min_idx] = min(abs(residuals));
    value = candidates(min_idx);
end

function residual = compute_color_difference_laplacian(bayer, G_interp, i, j, candidate, laplacian_kernel, channel, pattern)
% 计算颜色差值的拉普拉斯残差
    [h, w] = size(bayer);
    residual = 0;
    
    % 计算颜色差值
    color_diff = zeros(3,3);
    for di = -1:1
        for dj = -1:1
            ni = i + di;
            nj = j + dj;
            if ni >= 1 && ni <= h && nj >= 1 && nj <= w
                if strcmpi(channel, 'red')
                    channel_val = get_red_value(bayer, pattern, ni, nj);
                else
                    channel_val = get_blue_value(bayer, pattern, ni, nj);
                end
                
                if channel_val == 0 && di == 0 && dj == 0
                    % 中心位置使用候选值
                    color_diff(di+2, dj+2) = candidate - G_interp(ni, nj);
                elseif channel_val > 0
                    color_diff(di+2, dj+2) = channel_val - G_interp(ni, nj);
                else
                    % 估计缺失的值
                    color_diff(di+2, dj+2) = 0;
                end
            end
        end
    end
    
    % 计算拉普拉斯
    laplacian_val = sum(sum(color_diff .* laplacian_kernel));
    residual = abs(laplacian_val);
end

function value = get_red_value(bayer, pattern, i, j)
% 获取红色通道值
    [R, ~, ~] = extract_bayer_channels(bayer, pattern);
    value = R(i, j);
end

function value = get_blue_value(bayer, pattern, i, j)
% 获取蓝色通道值
    [~, ~, B] = extract_bayer_channels(bayer, pattern);
    value = B(i, j);
end

function image_out = handle_boundaries(image_in)
% 边界处理
    image_out = image_in;
    [h, w] = size(image_in);
    
    % 复制边界像素
    image_out(1,:) = image_out(2,:);
    image_out(h,:) = image_out(h-1,:);
    image_out(:,1) = image_out(:,2);
    image_out(:,w) = image_out(:,w-1);
    
    % 角落像素
    image_out(1,1) = image_out(2,2);
    image_out(1,w) = image_out(2,w-1);
    image_out(h,1) = image_out(h-1,2);
    image_out(h,w) = image_out(h-1,w-1);
end

高级改进版本

function [rgb_image] = improved_mlri_demosaic(bayer_image, pattern)
% 改进的MLRI去马赛克算法
    if nargin < 2
        pattern = 'rggb';
    end
    
    % 预处理：噪声抑制
    bayer_denoised = medfilt2(bayer_image, [3, 3]);
    
    % 主MLRI算法
    rgb_initial = mlri_demosaic(bayer_denoised, pattern);
    
    % 后处理：伪彩色抑制
    rgb_image = false_color_suppression(rgb_initial, bayer_denoised, pattern);
    
    % 边缘增强
    rgb_image = edge_enhancement(rgb_image);
end

function rgb_out = false_color_suppression(rgb_in, bayer, pattern)
% 伪彩色抑制
    rgb_out = rgb_in;
    [h, w, ~] = size(rgb_in);
    
    % 计算颜色梯度
    for i = 2:h-1
        for j = 2:w-1
            % 检测边缘区域
            edge_strength = compute_edge_strength(rgb_in, i, j);
            
            if edge_strength > 0.1 % 边缘区域
                % 应用方向自适应滤波
                rgb_out(i,j,:) = directional_filter(rgb_in, bayer, i, j, pattern);
            end
        end
    end
end

function edge_strength = compute_edge_strength(rgb, i, j)
% 计算边缘强度
    g_channel = rgb(:,:,2); % 绿色通道通常有最好的边缘信息
    
    % Sobel算子
    sobel_x = [-1, 0, 1; -2, 0, 2; -1, 0, 1];
    sobel_y = [-1, -2, -1; 0, 0, 0; 1, 2, 1];
    
    patch = g_channel(i-1:i+1, j-1:j+1);
    gx = sum(sum(patch .* sobel_x));
    gy = sum(sum(patch .* sobel_y));
    
    edge_strength = sqrt(gx^2 + gy^2);
end

function filtered_pixel = directional_filter(rgb, bayer, i, j, pattern)
% 方向自适应滤波
    % 根据局部梯度方向选择滤波方向
    g_channel = rgb(:,:,2);
    
    % 计算水平和垂直梯度
    h_grad = abs(g_channel(i,j-1) - g_channel(i,j+1));
    v_grad = abs(g_channel(i-1,j) - g_channel(i+1,j));
    
    if h_grad < v_grad
        % 水平方向滤波
        filtered_pixel = mean(rgb(i, j-1:j+1, :), 2);
    else
        % 垂直方向滤波
        filtered_pixel = mean(rgb(i-1:i+1, j, :), 1);
    end
    
    filtered_pixel = squeeze(filtered_pixel)';
end

function rgb_out = edge_enhancement(rgb_in)
% 边缘增强
    % 使用非锐化掩模
    h = fspecial('gaussian', [5, 5], 1.0);
    rgb_blur = imfilter(rgb_in, h, 'replicate');
    
    % 非锐化掩模
    rgb_out = rgb_in + 0.6 * (rgb_in - rgb_blur);
    rgb_out = min(max(rgb_out, 0), 1);
end

性能评估函数

function evaluate_demosaic(original_rgb, bayer_image, demosaiced_image, pattern)
% 评估去马赛克算法性能
    
    % PSNR计算
    mse = mean((original_rgb(:) - demosaiced_image(:)).^2);
    psnr = 10 * log10(1 / mse);
    
    % SSIM计算
    ssim_val = ssim(demosaiced_image, original_rgb);
    
    % 伪彩色指数计算
    fci = compute_false_color_index(demosaiced_image);
    
    fprintf('性能评估结果:\n');
    fprintf('PSNR: %.2f dB\n', psnr);
    fprintf('SSIM: %.4f\n', ssim_val);
    fprintf('伪彩色指数: %.4f\n', fci);
    
    % 可视化比较
    figure('Position', [100, 100, 1200, 400]);
    
    subplot(1,3,1);
    imshow(original_rgb);
    title('原始图像');
    
    subplot(1,3,2);
    bayer_display = repmat(bayer_image, [1, 1, 3]);
    imshow(bayer_display);
    title('Bayer模式图像');
    
    subplot(1,3,3);
    imshow(demosaiced_image);
    title('MLRI去马赛克结果');
end

function fci = compute_false_color_index(rgb_image)
% 计算伪彩色指数
    [h, w, ~] = size(rgb_image);
    
    % 计算颜色通道间的相关性
    r_channel = rgb_image(:,:,1);
    g_channel = rgb_image(:,:,2);
    b_channel = rgb_image(:,:,3);
    
    % 高通滤波检测异常颜色变化
    hp_filter = [-1, -1, -1; -1, 8, -1; -1, -1, -1] / 8;
    
    r_hp = imfilter(r_channel, hp_filter, 'replicate');
    g_hp = imfilter(g_channel, hp_filter, 'replicate');
    b_hp = imfilter(b_channel, hp_filter, 'replicate');
    
    % 伪彩色指数
    fci = mean(abs(r_hp - g_hp) + abs(r_hp - b_hp) + abs(g_hp - b_hp), 'all');
end

使用示例

% 主测试程序
function demo_mlri_demosaic()
    % 生成测试图像或加载真实Bayer图像
    original_rgb = im2double(imread('test_image.jpg'));
    
    % 转换为Bayer模式
    bayer_image = rgb2bayer(original_rgb, 'rggb');
    
    % 应用MLRI去马赛克
    tic;
    demosaiced_image = improved_mlri_demosaic(bayer_image, 'rggb');
    time_elapsed = toc;
    
    fprintf('MLRI去马赛克完成，耗时: %.2f秒\n', time_elapsed);
    
    % 性能评估
    evaluate_demosaic(original_rgb, bayer_image, demosaiced_image, 'rggb');
end

function bayer = rgb2bayer(rgb, pattern)
% 将RGB图像转换为Bayer模式
    [h, w, ~] = size(rgb);
    bayer = zeros(h, w);
    
    switch lower(pattern)
        case 'rggb'
            bayer(1:2:end, 1:2:end) = rgb(1:2:end, 1:2:end, 1); % R
            bayer(1:2:end, 2:2:end) = rgb(1:2:end, 2:2:end, 2); % G
            bayer(2:2:end, 1:2:end) = rgb(2:2:end, 1:2:end, 2); % G
            bayer(2:2:end, 2:2:end) = rgb(2:2:end, 2:2:end, 3); % B
    end
end

% 运行演示
demo_mlri_demosaic();

参考代码 利用最小拉普拉斯残差插值的去马赛克算法 www.youwenfan.com/contentcnm/82205.html

算法优势

1. 高质量的边缘保持：通过最小化拉普拉斯残差，在边缘区域选择最优插值方向
2. 伪彩色抑制：基于颜色通道相关性的插值减少伪彩色 artifacts
3. 计算效率：相比一些复杂方法，MLRI在质量和计算复杂度间取得良好平衡
4. 适应性：可适应不同的Bayer模式

这种算法特别适合需要高质量图像恢复的数码摄影和计算机视觉应用。