Noisy Recovery in Unlimited Sampling via Adaptive Modulo Representations

Recent works put forth the Unlimited Sensing Framework (USF), a novel approach to analog-to-digital conversion for high dynamic range sensing. It addresses the saturation phenomenon that commonly arises when physical measurements exceed the dynamic range of a sensor, yielding permanent loss of the input data. However, the USF still has some limitations when dealing with random noise. In the present paper, we propose a novel iterative method to tackle unlimited sensing in a noisy setting. In one step, our approach applies local transformations of the range to remove strong artifacts caused by the noise on local subdivisions of the domain. In the following step, the signal is then approximated via a least squares method. These two types of steps are then alternated. We illustrate the performances of our algorithm in high noise regime.