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.

翻译：在图像监控领域已有大量研究成果的背景下，目前仍缺乏指导从业者选择适当监控流程的数据驱动工具。参数选择的随意性所导致的潜在模型失配，可能使经验检测延迟偏离理论分析结果，并影响诊断预测的准确性。在图像监控中，潜在异常的稀疏度是许多监控流程开发所高度依赖的关键属性之一。本文提出一种计算友好的稀疏度指标——修正霍耶指数（corrected Hoyer index），用于估计受噪声干扰的潜在异常稀疏度。我们从理论上证明了所构建稀疏度指标的一致性，并通过仿真实验验证其一致性及对噪声的鲁棒性。此外，我们还阐释了如何将该稀疏度指标应用于实际工业场景的指导性见解。