A compressed sensing measurement matrix for atomic force microscopy

This work develops a novel sensing matrix for the application of compressed sensing (CS) to image acquisition in atomic force microscopy (AFM), with the goal of improving the temporal resolution of the instrument by reducing the amount of data that needs to be acquired to create a high-quality image. In traditional CS, each measurement is, by design, a linear combination of the elements of the signal under study. In AFM however, the physics of the sensing process require that each measurement contains information about only a single point. The measurement matrix introduced here takes this into account and allows the user to balance image acquisition time against image quality. The proposed method is demonstrated through simulation. These simulations show faithful recovery with a reduction in imaging time on the order of a factor of five. By accepting a reduction in image reconstruction quality, additional gains in imaging time of ten times or more, were achieved.