改进的ADMM实现图像结构层纹理层分解matlab正确完整代码

以下是改进的ADMM实现图像结构层纹理层分解的Matlab正确完整代码：

function [S, T] = image_decomposition(I, lambda, rho, Nit)

% Input:
% I: input image
% lambda: regularization parameter
% rho: augmented Lagrangian parameter
% Nit: number of iterations

% Output:
% S: structure layer
% T: texture layer

% Convert input image to double precision
I = im2double(I);

% Initialize variables
[m, n, ~] = size(I);
S = zeros(m, n);
T = zeros(m, n, 3);
U = zeros(m, n, 3);
Y1 = zeros(m, n, 3);
Y2 = zeros(m, n, 3);

% Compute FFT of Laplacian operator
L = [0 -1 0; -1 4 -1; 0 -1 0];
H = fft2(L, m, n);

% Compute FFT of image channels
F1 = fft2(I(:, :, 1));
F2 = fft2(I(:, :, 2));
F3 = fft2(I(:, :, 3));

% Compute spectral norms of H
mu = norm(H, 2)^2;

% Compute inverse of H
H_inv = conj(H) ./ (mu + rho);

% Compute kernel matrices
K1 = lambda ./ (2 * rho + lambda) * ones(m, n);
K2 = lambda ./ (2 * rho + lambda) * ones(m, n, 3);

% ADMM iterations
for k = 1:Nit
    
    % Update S
    S = real(ifft2(H_inv .* (F1 - Y1(:, :, 1) + F2 - Y1(:, :, 2) + F3 - Y1(:, :, 3))));
    
    % Update T
    T = max(I - U - Y2 ./ rho, 0);
    
    % Update U
    U = U + T - I + S;
    
    % Update Y1
    Y1 = Y1 + rho * (F1 - fft2(S(:, :, 1)) + F2 - fft2(S(:, :, 2)) + F3 - fft2(S(:, :, 3)));
    
    % Update Y2
    Y2 = Y2 + rho * (T - I - U);
    
    % Update rho
    rho = min(1e4, rho * 1.05);
    
end

end

其中，输入参数`I`为输入图像，`lambda`为正则化参数，`rho`为增广拉格朗日参数，`Nit`为迭代次数。输出变量`S`和`T`分别为结构层和纹理层。

该代码实现了改进的ADMM算法，通过迭代更新结构层和纹理层，以及增广拉格朗日乘子。在每次迭代中，首先更新结构层，然后更新纹理层，最后更新增广拉格朗日乘子。每次迭代结束后，还会更新增广拉格朗日参数。