Abstract:
A fundamental problem in signal analysis is the recovery of an object from clipped or saturated measurements. The latter refers to the effect that measurement devices can only measure quantities within a certain range. A classical example is the recording of audio, where sound can only be captured within a specific decibel range. The problem of recovering an object from clipped or saturated measurements is known as declipping or saturation recovery. The authors of the recent paper [W. Alharbi, D. Freeman, D. Ghoreishi, B. Johnson, N. L. Randrianarivony, Declipping and the recovery of vectors from saturated measurements, arXiv:2402.03237 (2024)] establish a rigorous mathematical framework for this problem in terms of frame theory. The purpose of this talk is to provide a self-contained introduction to saturation recovery and to discuss the main results of the aforementioned article.