Kolmogorov superposition theorem for image compression

The authors present a novel approach for image compression based on an unconventional representation of images. The proposed approach is different from most of the existing techniques in the literature because the compression is not directly performed on the image pixels, but is rather applied to an equivalent monovariate representation of the wavelet-transformed image. More precisely, the authors have considered an adaptation of Kolmogorov superposition theorem proposed by Igelnik and known as the Kolmogorov spline network (KSN), in which the image is approximated by sums and compositions of specific monovariate functions. Using this representation, the authors trade the local connectivity and the traditional line-per-line scanning, in exchange of a more adaptable and univariate representation of images, which allows to tackle the compression tasks in a fundamentally different representation. The contributions lie in the several strategies presented to adapt the KSN algorithm, including the monovariate construction, various simplification strategies, the proposal of a more suitable representation of the original image using wavelets and the integration of this scheme as an additional layer in the JPEG 2000 compression engine, illustrated for numerous images at different bit rates.