Variational Image Decomposition

Variational models for image decomposition

Image decomposition aims to separate an image into visually meaningful components whose superposition reconstructs the original. Our methods enable each component to be processed, analyzed, or enhanced independently, with applications in denoising, texture separation, and image editing.

Image Decomposition

We developed an efficient and effective three-component (cartoon-smooth-oscillation) image decomposition variational model. [Code]
We proposed a family of Vectorial Total Symmetric Variation (VTSV) for efficiently coupling channel information during decomposition.

References

(He et al., 2026) (He et al., 2025) (He & Liu, 2025)

References

2026

  1. Vectorial Total Symmetric Variation and Applications to Color Image Decomposition
    Roy Y He, Martin Huska, and Hao Liu
    2026

2025

  1. Image Decomposition with G-Norm Weighted by Total Symmetric Variation
    Roy Y He, Martin Huska, and Hao Liu
    In International Conference on Scale Space and Variational Methods in Computer Vision, 2025
  2. Euler’s elastica-based cartoon-smooth-texture image decomposition
    Roy Y He and Hao Liu
    SIAM Journal on Imaging Sciences, 2025