fit multiple positive and negative 2d gaussians that exponentially decays over time in matlab in matlab in matlab

To fit multiple positive and negative 2D Gaussians that exponentially decay over time in MATLAB, you can follow these steps:

1. Define the function representing the Gaussian distribution with exponential decay. This function should take the variables (x, y, t) as inputs and return the value of the 2D Gaussian at those coordinates and time.

main.m
function gauss = gaussian2D(x, y, t, A, x0, y0, sigma, tau)
    gauss = A * exp(-((x-x0).^2 + (y-y0).^2)/(2*sigma^2)).*exp(-t/tau);
end
136 chars
4 lines

2. Generate a grid of x, y, and t coordinates to form the input space where the Gaussians will be fitted.

main.m
[x, y, t] = meshgrid(x_range, y_range, t_range);
49 chars
2 lines

3. Load your data into a matrix or array, representing the intensity values of your distribution at each (x, y, t) coordinate.

main.m
data = load('data.mat');
intensity = data.intensity;
53 chars
3 lines

4. Use the lsqcurvefit function to fit the multiple Gaussians to the data. This function minimizes the sum of squares between the model and the data.

main.m
% Define the initial parameters for the Gaussians
initial_params = [A1, x01, y01, sigma1, tau1, A2, x02, y02, sigma2, tau2, ...];

% Create the anonymous function that will be fitted
fun = @(params) gaussian2D(x, y, t, params(1), params(2), params(3), params(4), params(5)) + ...
                gaussian2D(x, y, t, params(6), params(7), params(8), params(9), params(10)) + ...;

% Perform the fitting
fit_params = lsqcurvefit(fun, initial_params, [x(:), y(:), t(:)], intensity(:));
483 chars
10 lines

5. Once the fitting is done, you can extract the parameters for each Gaussian and use them for further analysis or plotting.

main.m
% Extract the parameters for each Gaussian
A1 = fit_params(1);
x01 = fit_params(2);
y01 = fit_params(3);
sigma1 = fit_params(4);
tau1 = fit_params(5);
151 chars
7 lines

Note that this code assumes you have already loaded your data into a 3D matrix called intensity. You also need to define the ranges of your x, y, and t variables in the meshgrid step.

Remember to modify the code according to your specific needs, such as adding more Gaussians or changing the initial parameters.

I hope this helps you fit multiple positive and negative 2D Gaussians that exponentially decay over time in MATLAB!