Define Gaussian point spread function

I want to define a point spread function as a Gaussian. I know the amplitude, sigma and mu for the Gaussian. How do I generate a PSF from those parameters? I would then like to use the PSF in the Lucy-Richardson deblurring algorithm.

I am thinking to define: PSF = imgaussfilt(Image, sigma), but this only allows me to define sigma.

Is there a MATLAB function that allows me to define the amplitude, sigma and mu for the Gaussian function?

Thank you.

Answer 1

[Abhaya]

Hi LM,

Based on my understanding, you want to define a Gaussian point spread function (PSF) using the amplitude, sigma, and mean (mu) as parameters.

To achieve this, you can use one of the following methods:

• You can create a custom function to generate a Gaussian PSF using the given parameters. Below is a sample function:

function psf = createGaussianPSF(amplitude, sigma, mu, size)
    %create a grid of points
    [x, y] = meshgrid(-(size(2)-1)/2:(size(2)-1)/2, -(size(1)-1)/2:(size(1)-1)/2);
    mu_x = mu(1);
    mu_y = mu(2);
    
    %create custom PSF
    PSF = amplitude * exp(-((x - mu_x).^2 + (y - mu_y).^2) / (2 * sigma^2));    
    PSF = circshift(PSF, [mu_y, mu_x]);
end

• You can create a Gaussian PSF using MATLAB 'fspecial' function and adjust it according to your parameters:

PSF = fspecial('gaussian', hsize, sigma); 
PSF = amplitude * PSF; 
shift_x = mu(1);
shift_y = mu(2); 
PSF = circshift(PSF, [shift_y, shift_x]);

To apply Lucy-Richardson deblurring algorithm, you can use MATLAB 'deconvlucy' function.

For more information, please refer to the following MATLAB documentations for ‘circshift’, ‘fspecial’ and ‘deconvlucy’ functions, respectively.

• https://www.mathworks.com/help/matlab/ref/circshift.html
• https://www.mathworks.com/help/images/ref/fspecial.html
• https://www.mathworks.com/help/images/ref/deconvlucy.html

Hope this solves your query.