Parametric and nonparametric approaches to detection in magnetic resonance force microscopy

We address signal detection in magnetic resonance force microscopy (MRFM) and single spin microscopy (SESM). MRFM and SESM are considered as a promising technology to provide nondestructive and atomic-scale imaging. From a signal processing point of view, the main challenge is to extract very weak signals from measurements with a signal to noise ratio (SNR) typically less than -15 dB. We investigate two detection schemes based different features of the underlying system. The parametric approach is derived from the generalized likelihood ratio test (GLRT). The nonparametric approach exploits the spectral property of the observation. Numerical experiments show that both detectors provide excellent results at very low SNRs.