Does anything interesting happen if you take the frequency domain representation of an image, represent the frequency domain as an image itself, and compress that with some sort of image compression? For example, encode the frequency domain representation as a low quality JPEG, and then undo the steps to turn it back into the "original". How do the JPEG artifacts on the frequency domain manifest in the resulting imag…
This wouldn't work well because in the frequency domain representation, different "pixels" have very different importance for the overall appearance of the image: The pixels at the center of the frequency domain representation represent low frequencies, so compressing them will drastically alter the appearance of the image. On the other hand, the corners/edges of the frequency domain representation represent high fre…
But if the original data is an image (matrix or grid of pixels in space), then the "frequency domain pixels" are different wave-numbers (aka spatial frequencies: how many repetitions in a meter, etc.) and the Fourier transform (of the pixel grid) is a amplitude vs. wave-number function.