Unlimited Sampling with Hysteresis

The Unlimited Sensing Framework (USF) addresses the problem of sensor saturation in analog-to-digital converters. In essence, the USF maps high-dynamic-range (HDR) signals into low-dynamic-range (LDR) samples via a non-linear, modulo sampling operator, folding the input whenever it reaches the modulo threshold. However, some assumptions of the USF may require a careful hardware calibration which can lead to an increased implementation complexity. At the interface of theory and practice, here we propose a computational sampling strategy in order to add more flexibility to the circuit design specifications. Specifically, we introduce a new model for USF with two additional degrees of freedom describing the effects of hysteresis and folding transients. The hysteresis is a memory effect determined by a mismatch between the modulo reset threshold and amplitude displacement, and the folding transients are transition periods associated with each reset time. We provide a theoretically guaranteed reconstruction method based on thresholding for the newly introduced model. We validate our method in a numerical study. Therefore the proposed methodology motivates a computational sampling approach for HDR signal reconstruction, enabling a reduced complexity of hardware.