# Mixed Graph Signal Analysis of Joint Image Denoising / Interpolation

arXiv: https://arxiv.org/abs/2309.10114 · HTML: https://mlsanity.com/paper/2309.10114/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2023.

## Built on by (most cited first, 3 of 3)

- [Latent Space Score-based Diffusion Model for Probabilistic Multivariate Time Series Imputation](https://mlsanity.com/paper/2409.08917/) (2024)
- [Constructing an Interpretable Deep Denoiser by Unrolling Graph Laplacian Regularizer](https://mlsanity.com/paper/2409.06676/) (2024)
- [Unrolling Graph-based Douglas-Rachford Algorithm for Image Interpolation with Informed Initialization](https://mlsanity.com/paper/2509.11926/) (2025)

## Abstract (arXiv)

A noise-corrupted image often requires interpolation. Given a linear denoiser and a linear interpolator, when should the operations be independently executed in separate steps, and when should they be combined and jointly optimized? We study joint denoising / interpolation of images from a mixed graph filtering perspective: we model denoising using an undirected graph, and interpolation using a directed graph. We first prove that, under mild conditions, a linear denoiser is a solution graph filter to a maximum a posteriori (MAP) problem regularized using an undirected graph smoothness prior, while a linear interpolator is a solution to a MAP problem regularized using a directed graph smoothness prior. Next, we study two variants of the joint interpolation / denoising problem: a graph-based denoiser followed by an interpolator has an optimal separable solution, while an interpolator followed by a denoiser has an optimal non-separable solution. Experiments show that our joint denoising / interpolation method outperformed separate approaches noticeably.