about fourier transform

what is the best reconstruction in term of quality of the image when using fft2 and ifft2 without pre and post processing.

[Sean de Wolski]

What do you mean "What is the best reconstruction?" Explain your question and you'll get better answers.

[si kijang]

Example,if use Radon,the values of angle determine how good result we can get.For Zernike moments,the order will be the manipulated variable. But for fourier i don't know what are the manipulated variables.

Answer 1

[Walter Roberson]

Are you asking: "If I have an image and I fft2() the image, and I ifft2() the result of that, then what is the maximum difference I should expect for any one pixel compared between the original and reconstructed image" ?

[si kijang]

yes,but i also want ask about:

Example,if use Radon,the values of angle determine how good result we can get.For Zernike moments,the order will be the manipulated variable. But for fourier i don't know what are the manipulated variables.

Answer 2

[David Young]

The Discrete Fourier Transform has no parameters to manipulate. The difference between the original and the reconstructed images will always be very small, though non-zero because of rounding errors.

You could explore this experimentally with test code similar to this:

imsize = 100 + ceil(1000*rand);
img = rand(imsize);
ft = fft2(img);
recon = ifft2(ft);
max(abs(img(:)-recon(:)))

which typically produces a result of order 1e-15 on my system.

[Walter Roberson]

From one point of view at least, the parameter for fft would be the number of fft bins to use, and the best would be the same as the number of points along that dimension.