The Likelihood Ratio Test for the Multiple Signals Model for Signal Detection from fMRI Brain Images

Thomas M. Menino Convention & Exhibition Center 

We developed a likelihood ratio test for detecting multiple signals in functional magnetic resonance imaging (fMRI) brain images, extending classical single-signal detection methods. Using the framework of reproducing kernel Hilbert spaces, we derive the test statistic \( Y_{{\text{max}}} \) for the multiple signals model, generalizing prior approaches that utilized global maxima for signal detection. A computationally robust alternative, \( U_{{\text{max}}} \), is also introduced. The performance of these test statistics is evaluated through extensive simulation studies under varying image resolutions, sample sizes, and signal configurations. The results demonstrate that \( Y_{{\text{max}}} \) offers superior sensitivity compared to traditional \( X^2_{{\text{max}}} \) statistic, particularly under complex multi-signal scenarios. Feature importance analysis using Random Forest regression reveals that image resolution significantly impacts test outcomes. These findings provide a robust statistical tool for improved activation detection in neuroimaging applications.

Gaussian Random Field, Scale Space, Multiple Signals Model, Likelihood Ratio Test, Reproducing Kernel Hilbert Space, fMRI, Signal Detection, Simulation Study 

IMS