in an ideal world, an image is piecewise smooth. it has soft gradients, some detail and edges. in particular there’s no noise and the edges are sharp. given these assumptions, you can do a lot of cool things to your pictures, using techniques like frequency space editing, wavelets, or local histograms.
darktable’s equalizer module demonstrates some of this, using the wavelet approach. you can use it to sharpen and denoise, enhance or attenuate certain frequencies in your image, while keeping the edges intact.