# Objective function required for genetic allgorithm

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Rizwan Khan on 7 Aug 2019
Answered: Prateekshya on 22 Jul 2024 at 8:23
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)

Prateekshya on 22 Jul 2024 at 8:23
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');
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.