Piezoresponse force microscopy (PFM) is a scanning microscopy technique that is used to evaluate the nanoscale strain response to an electric voltage applied to the surface of a ferroelectric material. PFM is a powerful tool for imaging, manipulation, and studying the nanoscale functional response of ferroelectric materials, which has been extensively used as a first pass test for ferroelectricity in novel materials with unknown functional properties. However, low signal-to-noise ratio observations arising from the loss of electromechanical signal during polarization switching often result in unreliable information extraction at these observations, hampering our understanding of the material characteristics. To address this challenge, we propose an information recovery framework utilizing subspace-based matrix completion to achieve improved characterization from PFM data. It enables us to efficiently recover and extract reliable information from the data, assisting the modeling efforts for PFM and providing insights for characterization and experimentation practices.