Improved Recovery Guarantees for One-Bit Unlimited Sampling

The Unlimited Sensing Framework (USF) was recently introduced as an alternative for capturing high-dynamic-range analog signals. It incorporates a modulo non-linearity prior to sampling and algorithmically unfolds the signal during the reconstruction step, thus avoiding problems caused by sensor saturation. In this paper, we focus on the quantization problem in the context of USF. We build upon the existing method which enables reconstruction from 1-bit modulo samples obtained via Sigma-Delta quantization. We show that by implementing some changes in the acquisition scheme it is possible to enhance the reconstruction accuracy to the extent that the modulo folding introduces no additional error contribution.