Non-linear spectral decompositions of images based on one-homogeneous functionals such as total variation have gained considerable attention in the last few years. Due to their ability to extract spectral components corresponding to objects of different size and contrast, such decompositions enable filtering, feature transfer, image fusion and other applications. However, obtaining this decomposition involves solving multiple non-smooth optimisation problems and is therefore computationally highly intensive. To overcome this issue, we look at training a neural network to reproduce the spectral total variation decomposition at a considerably reduced computational cost. Since the total variation transform can be seen as a non-linear analogue to the Fourier transform, we aim to obtain an analogue to the Fast Fourier Transform in our approach. The availability of a fast computational method is arguably one of the reasons for the success of the Fourier transform in signal and image processing. Fast methods for non-linear spectral decomposition therefore have the potential to become an equally important tool for image and data analysis.
Joint work with Guy Gilboa (Technion).