Cartoon-texture image decomposition is a critical preprocessing problem bottlenecked by the numerical intractability of classical variational or optimization models and the tedious manual tuning of global regularization parameters.We propose a Guided Variational Decomposition (GVD) model which introduces spatially adaptive quadratic norms whose pixel-wise weights are learned either through local probabilistic statistics or via a lightweight neural network within a bilevel framework.This leads to a unified, interpretable, and computationally efficient model that bridges classical variational ideas with modern adaptive and data-driven methodologies. Numerical experiments on this framework, which inherently includes automatic parameter selection, delivers GVD as a robust, self-tuning, and superior solution for reliable image decomposition.
@article{arxiv.2601.04999,
title = {Guided Variational Network for Image Decomposition},
author = {Alessandro Lanza and Serena Morigi and Youwei Wen and Li Yang},
journal= {arXiv preprint arXiv:2601.04999},
year = {2026}
}