Superresolution through regular sampling: Theory and applications

Abstract

Estimating fine-scale spectral information from coarse-scale measurements is an important issue in many signal processing applications. The problem of superresolution is therefore receiving considerable attention. We offer a technique that allows to overcome the Shannon-Nyquist sampling rate limitation and at the same time may improve the conditioning of the numerical linear algebra problems involved. The technique is exploiting aliasing rather than avoiding it and maintains a regular sampling scheme [3]. It relies on the concept of what we call an identification shift [1, 2], which is the additional sampling at locations shifted with respect to the original locations in order to overcome any ambiguity in the analysis. Neither the original sampling nor the identification shift need to respect the Shannon-Nyquist sampling theorem. So far the technique shows great potential in magnetic resonance spectroscopy, vibration analysis, echolocation, music signal processing, ISAR radar problems, and DOA or direction of arrival. [1] Annie Cuyt and Wen-shin Lee, “Smart data sampling and data reconstruction,” US patent 9,690,749. [2] Annie Cuyt and Wen-shin Lee, “Smart data sampling and data reconstruction,” EP2745404B1. [3] Annie Cuyt and Wen-shin Lee, “How to get high resolution results from sparse and coarsely sampled data,” ArXiv e-print 1710.09694 [math.NA].Estimating fine-scale spectral information from coarse-scale measurements is an important issue in many signal processing applications. The problem of superresolution is therefore receiving considerable attention. We offer a technique that allows to overcome the Shannon-Nyquist sampling rate limitation and at the same time may improve the conditioning of the numerical linear algebra problems involved. The technique is exploiting aliasing rather than avoiding it and maintains a regular sampling scheme [3]. It relies on the concept of what we call an identification shift [1, 2], which is the additional sampling at locations shifted with respect to the original locations in order to overcome any ambiguity in the analysis. Neither the original sampling nor the identification shift need to respect the Shannon-Nyquist sampling theorem. So far the technique shows great potential in magnetic resonance spectroscopy, vibration analysis, echolocation, music signal processing, ISAR radar problems, and DOA or directio...