# Spatial CUSUM for Signal Region Detection

## TL;DR

The paper introduces Spatial CUSUM (SCUSUM), a novel method for detecting weak clustered signals in spatial data, demonstrating high accuracy and sensitivity, especially in medical imaging applications.

## Contribution

The paper develops the SCUSUM method combining CUSUM and false discovery rate control, with theoretical properties and superior detection of weak signals compared to existing methods.

## Key findings

- SCUSUM achieves high classification accuracy asymptotically.
- SCUSUM is sensitive to weak spatial signals in simulations.
- SCUSUM detects more irregular weak signals in fMRI data than existing methods.

## Abstract

Detecting weak clustered signal in spatial data is important but challenging in applications such as medical image and epidemiology. A more efficient detection algorithm can provide more precise early warning, and effectively reduce the decision risk and cost. To date, many methods have been developed to detect signals with spatial structures. However, most of the existing methods are either too conservative for weak signals or computationally too intensive. In this paper, we consider a novel method named Spatial CUSUM (SCUSUM), which employs the idea of the CUSUM procedure and false discovery rate controlling. We develop theoretical properties of the method which indicates that asymptotically SCUSUM can reach high classification accuracy. In the simulation study, we demonstrate that SCUSUM is sensitive to weak spatial signals. This new method is applied to a real fMRI dataset as illustration, and more irregular weak spatial signals are detected in the images compared to some existing methods, including the conventional FDR, FDR$_L$ and scan statistics.