why below code takes longer time to execute, even with only one input image it takes longer time to execute.

We plan to use this code for 1000 images so it is very difficult to complete so any other way is there to do this.

Answer 1

[Guillaume]

You haven't vectorised any of your code. Try this:

function [Fcc,Fcs,Fsc,Fss]=fun_cosine_series2(f,u,v)
    a = pi * u / size(f, 1);
    b = pi * v / size(f, 2);
    rows = (1:size(f, 1)).';
    cols = 1:size(f, 2);
    cos1 = cos(a * (rows + 0.5));
    cos2 = cos(b * (cols + 0.5));
    sin1 = sin(a * (rows + 0.5));
    sin2 = sin(b * (cols + 0.5));
    Fcc = sum(sum(f .* cos1 .* cos2));
    Fcs = sum(sum(f .* cos1 .* sin2));
    Fsc = sum(sum(f .* sin1 .* cos2));
    Fss = sum(sum(f .* sin1 .* sin2));
end

It requires R2016b or later for implicit expansion, if you're on an earlier version replace all the sum(sum(f .* x .* y)) by

sum(sum(f .* bsxfun(@times, x, y)))

where x and y are the respective cos an sin vectors obviously.

[Stephen23]

For more information on code vectorization, and how to write efficient MATLAB code:

https://www.mathworks.com/help/matlab/matlab_prog/vectorization

https://www.mathworks.com/help/matlab/matlab_prog/techniques-for-improving-performance.html