Discrete denoising of heterogenous two-dimensional data

TL;DR

This paper extends a universal denoising algorithm from one-dimensional to two-dimensional data using quadtree decomposition and space-filling curves, achieving near-genie performance with linear complexity.

Contribution

It introduces a two-dimensional S-DUDE that adapts to regionally varying data characteristics, maintaining efficiency and competitive accuracy.

Findings

Performs nearly as well as a genie with access to noiseless data

Maintains linear complexity in data size and number of regions

Effective in denoising images with varying characteristics

Abstract

We consider discrete denoising of two-dimensional data with characteristics that may be varying abruptly between regions. Using a quadtree decomposition technique and space-filling curves, we extend the recently developed S-DUDE (Shifting Discrete Universal DEnoiser), which was tailored to one-dimensional data, to the two-dimensional case. Our scheme competes with a genie that has access, in addition to the noisy data, also to the underlying noiseless data, and can employ $m$ different two-dimensional sliding window denoisers along $m$ distinct regions obtained by a quadtree decomposition with $m$ leaves, in a way that minimizes the overall loss. We show that, regardless of what the underlying noiseless data may be, the two-dimensional S-DUDE performs essentially as well as this genie, provided that the number of distinct regions satisfies $m=o(n)$, where $n$ is the total size of the data. The resulting algorithm complexity is still linear in both $n$ and $m$, as in the one-dimensional case. Our experimental results show that the two-dimensional S-DUDE can be effective when the characteristics of the underlying clean image vary across different regions in the data.