fit 2d gaussian that exponentially decays over time in matlab in matlab

To fit a 2D Gaussian that exponentially decays over time in MATLAB, you can follow these steps:

  1. Define your 2D Gaussian function. The function should have four parameters: amplitude, center_x, center_y, and sigma. Here is an example of a 2D Gaussian function:
main.m
gaussian = @(x, y, params) params(1) * exp(-(x-params(2)).^2/(2*params(4)^2) - (y-params(3)).^2/(2*params(4)^2));

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  1. Generate a grid of x and y values that represents your image or data.

  2. Create your observed data. This can be the actual image data or any other data that you want to fit the Gaussian function to.

  3. Define an initial guess for the parameters of the 2D Gaussian function. This will help the fitting algorithm start from a reasonable point. For example:

main.m
initial_params = [1, size(data, 2)/2, size(data, 1)/2, 1];

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  1. Use the lsqcurvefit function in MATLAB to fit the Gaussian function to the observed data. Here is an example of how to use lsqcurvefit:
main.m
fit_params = lsqcurvefit(gaussian, initial_params, x_values, y_values, observed_data);

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  1. Once the fitting process is complete, you will have the best-fit parameters for the Gaussian function. You can then use these parameters to generate the fitted Gaussian curve:
main.m
fitted_data = gaussian(x_values, y_values, fit_params);

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  1. Finally, you can visualize the observed data and the fitted Gaussian curve using MATLAB's plotting functions.

Here is the complete code snippet that demonstrates the fitting process:

main.m
% Define the 2D Gaussian function
gaussian = @(x, y, params) params(1) * exp(-(x-params(2)).^2/(2*params(4)^2) - (y-params(3)).^2/(2*params(4)^2));

% Generate x and y values
[x_values, y_values] = meshgrid(1:size(data, 2), 1:size(data, 1));

% Create observed data
observed_data = % Your data here

% Define initial guess
initial_params = [1, size(data, 2)/2, size(data, 1)/2, 1];

% Fit the Gaussian function to the observed data
fit_params = lsqcurvefit(gaussian, initial_params, x_values, y_values, observed_data);

% Generate fitted Gaussian curve
fitted_data = gaussian(x_values, y_values, fit_params);

% Plot the observed data and fitted Gaussian curve
figure;
subplot(1, 2, 1);
imshow(observed_data);
title('Observed Data');
subplot(1, 2, 2);
imshow(fitted_data);
title('Fitted Gaussian');

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Note: Replace % Your data here with the actual data you want to fit the Gaussian to.

Hope this helps!

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