Quick and Consistent Sparsity Estimation for Streaming Images with Noise

TL;DR

This paper introduces a computationally efficient and noise-robust sparsity index for streaming image anomaly detection, improving monitoring accuracy by guiding practitioners in selecting appropriate procedures.

Contribution

It proposes the corrected Hoyer index, a new sparsity estimator with proven consistency and robustness, aiding real-world image monitoring applications.

Findings

The corrected Hoyer index is consistent in estimating sparsity.

The index demonstrates robustness against noise in simulations.

Guidelines are provided for practical application of the sparsity index.

Abstract

Given fruitful works in the image monitoring, there is a lack of data-driven tools guiding the practitioners to select proper monitoring procedures. The potential model mismatch caused by the arbitrary selection could deviate the empirical detection delay from their theoretical analysis and bias the prognosis. In the image monitoring, the sparsity of the underlying anomaly is one of the attributes on which the development of many monitoring procedures is highly based. This paper proposes a computational-friendly sparsity index, the corrected Hoyer index, to estimate the sparsity of the underlying anomaly interrupted by noise. We theoretically prove the consistency of the constructed sparsity index. We use simulations to validate the consistency and demonstrate the robustness against the noise. We also provide the insights on how to guide the real applications with the proposed sparsity index.