The discovery of quantum materials requires an experimental verification of their band-structure. Quasiparticle interference (QPI) imaging with the
scanning tunneling microscope can provide insight into the material’s properties when angle resolved photoelectron emission spectroscopy would be
limited due to low-temperature, magnetic field or too small devices. However, obtaining band-structure insight from QPI is very slow. Our method achieves several orders of magnitude faster mapping by a mutually beneficial
combination of sparse sampling and parallel spectroscopy whose effect exponentially amplify another. Our method cuts down the mapping time from weeks to minutes, enabling the faster characterization of materials and
exploration of previously impossibly larger parameter spaces.