Mixed Graph Signal Analysis of Joint Image Denoising / Interpolation

TL;DR

This paper models image denoising and interpolation using graph filters, proving conditions for optimal joint or separate processing, and demonstrates that joint methods outperform separate ones in experiments.

Contribution

It provides a theoretical framework for joint image denoising and interpolation using mixed graph filtering, identifying when combined optimization is advantageous.

Findings

Joint denoising/interpolation outperforms separate methods.

Linear denoiser and interpolator correspond to MAP solutions with graph regularization.

Separable and non-separable solutions depend on operation order.

Abstract

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.