Edge-enhancing Filters with Negative Weights

TL;DR

This paper extends graph Laplacian construction to include negative weights, enabling more accurate image denoising filters by better modeling the underlying data structure without increasing computational costs.

Contribution

It introduces a method to incorporate negative weights into graph Laplacians, improving graph-based denoising performance over traditional positive-weight models.

Findings

Negative weights enhance denoising quality

Improved graph modeling accuracy

No additional computational cost

Abstract

In [DOI:10.1109/ICMEW.2014.6890711], a graph-based denoising is performed by projecting the noisy image to a lower dimensional Krylov subspace of the graph Laplacian, constructed using nonnegative weights determined by distances between image data corresponding to image pixels. We~extend the construction of the graph Laplacian to the case, where some graph weights can be negative. Removing the positivity constraint provides a more accurate inference of a graph model behind the data, and thus can improve quality of filters for graph-based signal processing, e.g., denoising, compared to the standard construction, without affecting the costs.