We apply the Principal Component Inverse (PCI) method of rapidly adaptive interference suppression and signal detection to reverberation suppression and modeling. We present preliminary results for the challenging example in which the transmitted pulse is a two-second burst of hyperbolic frequency-modulated (HFM) sinusoid sweeping from 210 Hz to 280 Hz. We demonstrate improved detection performance after reverberation suppression, as compared to conventional matched filtering. We provide a physical interpretation of the principal components by presenting corresponding conventional and high-resolution temporal frequency/spatial frequency analysis of sets of snapshots from a subarray.