Is there transfomation that transform the image to a space that I can use a small amount of function of fit it?

Question

Now what I want to do is that I want to reprentation(just fitting) a image with neural network with as less error as possible,like paper NeRF(neural reprentation field) and FFN and Sire. The input is coordinat of image, output is the pixel value of image. Therefore, the neural network actually can fit the whole image. You just input the coordinate, and the neural network output is the image pixel at the specific coordinate. Now what I want to do is that i want to find a transformation. It transform a image to a space, so that in that space the coefficient is very smooth. That I can use just a small number of continious function to represent(fit) it. I tried with Fourier transform, however, the spectrum in the Fourier tramsform change sharply. Like image here. This is line profile of image Fourier spectrum magnitude. This signal definately is not easy to fit. (it vary in the order of millions). Even, after i applied a log scale to this signal, it is still not very easy to fit. It is like this. It change sharply. I want to have image transformation that after transformation, the image signal become very smooth or very easy to fit just by a small amount of functions. Do you have some advice? Thank you very much.