Random matrix DCSC colloquium

What happens when a finite number of signals are embedded in a high-dimensional noisy matrix? Can spectral methods such as PCA still detect them?

This work provides sharp bounds on the parameters required to detect one or more spikes through the extreme eigenvalues of the SMM covariance matrix. We establish critical thresholds, determined by the interplay between the spike parameters, above which extreme eigenvalues detach from the noise bulk and reveal the presence of signal structure.

These theoretical guarantees have potential implications for real-world detection problems described by this model, including hyperspectral imaging and imaging mass spectrometry.