Objective function required for genetic allgorithm

how to write objective function to optimize a signal:

F=K.F'+n

(f=catured image

f'=latent signal convolved with Point spread function +n is (Noise)

Answer 1

[Prateekshya]

Hello Rizwan,

I can help you write the objective function for optimizing a signal in MATLAB using Genetic Algorithm (GA). Here is an example for the same:

% Example captured image F (replace with actual data)
F = [...];  % Captured image data

% Example point spread function K (replace with actual data)
K = [...];

% Example noise n (replace with actual data)
n = [...];

% Define the objective function
function mse = objectiveFunction(f_prime, F, K, n)
    % Reshape f_prime to the size of the latent signal
    f_prime = reshape(f_prime, size(F));
    
    % Convolve the latent signal with the point spread function
    convolved_signal = conv2(f_prime, K, 'same');
    
    % Add noise
    model = convolved_signal + n;
    
    % Calculate the mean squared error
    mse = mean((F(:) - model(:)).^2);
end

% Define the initial guess for the latent signal
initial_guess = rand(size(F));

% Define the fitness function for the Genetic Algorithm
fitnessFunction = @(f_prime) objectiveFunction(f_prime, F, K, n);

% Set the Genetic Algorithm options
options = optimoptions('ga', 'PopulationSize', 20, 'MaxGenerations', 100, 'Display', 'iter');

% Run the Genetic Algorithm
[optimized_f_prime, fval] = ga(fitnessFunction, numel(F), [], [], [], [], [], [], [], options);

% Reshape the optimized latent signal to the original size
optimized_f_prime = reshape(optimized_f_prime, size(F));

% Display the optimized MSE
disp(['Optimized MSE: ', num2str(fval)]);

I have taken a few assumptions regarding the exact values. You may replace them according to your requirement.

I hope this helps!

Thank you.