Low-rank physical model recovery from low-rank signal approximation

Abstract

This work presents a mathematical approach for recovering a physical model from a low-rank approximation of measured data obtained via the singular value decomposition (SVD). The general form of a low-rank physical model of the data is often known, so the presented approach learns the proper rotation and scaling matrices from the singular vectors and singular values of the SVD in order to recover the low-rank physical model of the data from the SVD approximation. By recovering the low-rank physical model, it becomes possible to exploit specific knowledge of the model to extract meaningful information for the physical application being studied. This work is useful for processing wide-band electromagnetic induction data-the motivating application.