Infrared (IR) vibrational scattering scanning near-field optical microscopy (s-SNOM) has advanced to become a powerful nanoimaging and spectroscopy technique with applications ranging from biological to quantum materials. However, full spatiospectral s-SNOM continues to be challenged by long measurement times and drift during the acquisition of large associated datasets. Various embodiments provide for a novel approach of computational spatiospectral s-SNOM by transforming the basis from the stationary frame into the rotating frame of the IR carrier frequency. Some embodiments see acceleration of IR s-SNOM data collection by a factor of 10 or more in combination with prior knowledge of the electronic or vibrational resonances to be probed, the IR source excitation spectrum, and other general sample characteristics.