The Landweber and MART (Multiplicative Algebraic Reconstruction Technique) regularization methods are commonly used in image reconstruction and signal processing applications. Although specific implementations may vary, I can provide you with a general guideline to create MATLAB functions for these regularization methods:

1. Landweber Regularization:

The Landweber regularization method is an iterative algorithm for solving ill-posed inverse problems. Here's a basic MATLAB function that implements the Landweber method:

```matlab

function x = landweber(A, b, iterations, stepsize)

% A: System matrix

% b: Measured data vector

% iterations: Number of iterations

% stepsize: Step size or regularization parameter

[m, n] = size(A);

x = zeros(n, 1); % Initialize the solution vector

for iter = 1:iterations

% Update the solution using Landweber iteration formula

x = x - stepsize * A' * (A * x - b);

end

```

You need to provide the system matrix `A`, the measured data vector `b`, the number of iterations, and the step size (regularization parameter). The function updates the solution iteratively using the Landweber iteration formula.

2. MART Regularization:

The MART regularization method is an iterative technique commonly used in computed tomography (CT) image reconstruction. Here's a simple MATLAB function for implementing the MART algorithm:

```matlab

function x = mart(A, b, iterations)

% A: System matrix

% b: Measured data vector

% iterations: Number of iterations

[m, n] = size(A);

x = zeros(n, 1); % Initialize the solution vector

for iter = 1:iterations

% Update the solution using MART iteration formula

x = x .* (A' * (b ./ (A * x + eps))) ./ (A' * ones(m, 1));

end

```

You need to provide the system matrix `A`, the measured data vector `b`, and the number of iterations. The function performs the MART iterations, updating the solution based on the MART iteration formula.

Note: These are basic implementations, and you may need to modify them based on the specific problem you are solving. Additionally, consider incorporating suitable stopping criteria and handling specific constraints if required.

Remember to adapt these functions to your specific problem and matrix representations. Also, ensure that you have the necessary system matrix `A` and measured data vector `b` appropriately defined before using these functions.