Guided Variational Network for Image Decomposition

TL;DR

This paper introduces a Guided Variational Decomposition model that adaptively decomposes images into cartoon and texture components using learned spatial weights, combining classical variational methods with modern neural networks for improved efficiency and robustness.

Contribution

The paper presents a novel GVD model that integrates spatially adaptive quadratic norms with neural network-based weight learning within a bilevel framework, enabling automatic parameter tuning and superior image decomposition.

Findings

GVD outperforms traditional methods in image decomposition quality.

The model automatically learns spatial weights, reducing manual tuning.

Numerical experiments demonstrate robustness and efficiency of GVD.

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.