Unlimited Sampling with Sparse Outliers: Experiments with Impulsive and Jump or Reset Noise

Unlimited Sensing is a sampling protocol that recovers high dynamic range input signals from their low dynamic range, modulo samples. Bridging the gap between theory and practice, recently, a hardware validation of the unlimited sampling method was presented. Taking another step in this direction, in this paper, we study the problem of recovery from modulo samples contaminated by sparse outliers (noise). Our hardware experiments suggest that impulsive and jump or reset noise can be sources of sparse outliers in the measurements. Such a noise model has not been considered in literature and can lead to the breakdown of the conventional recovery methods. To overcome this problem, we present a mathematically guaranteed algorithm that is based on spectral estimation. Our method perfectly recovers the signal (up to a constant) when the sampling criterion is met and no other noise sources are present. In real experiments where quantization and system noise (e.g. additive Gaussian) play a role, our approach offers a competitive performance. Hardware experiments with our modulo ADC validate the practical utility of our method.