Guided Variational Network for Image Decomposition

2026/01/31 by Alessandro Lanza, Serena Morigi, Youwei Wen +1
Mathematics · Computer Science · #math.NA #cs.NA

paper · pdf

Code is publicly available at https://github.com/yangli161029/NGVD

arxiv created 2026/07/31 · arxiv updated 2026/08/03

Abstract

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.

Citations

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