Detection of Geometric Structures by an Optimally Subsampled Shearlet System in Noisy Digital Images

TL;DR

This paper analyzes how digitized shearlet systems can detect objects in noisy digital images and explores subsampling methods to maintain detection performance with fewer elements.

Contribution

It introduces a statistical framework for subsampling shearlet systems while preserving optimal detection capabilities in noisy environments.

Findings

Subsampling shearlet systems retains detection performance.

Reduced shearlet systems significantly lower computational complexity.

Detection in noisy images remains statistically optimal after subsampling.

Abstract

We provide a statistical analysis of the ability of digitized continuous shearlet systems to detect objects embedded in white noise. We analyze the possibility to subsample the shearlet transform and obtain a subset of significantly reduced cardinality that can still yield statistically optimal detection results.