  Recent results in one-bit sampling provide a framework for a relatively
low-cost, low-power sampling, at a high rate by employing time-varying sampling
threshold sequences. Another recent development in sampling theory is unlimited
sampling, which is a high-resolution technique that relies on self-reset ADCs
to yield an unlimited dynamic range. In this paper, we leverage the appealing
attributes of the two aforementioned techniques to propose a novel
\emph{un}limited \emph{o}ne-bit (UNO) sampling approach. In this framework, the
information on the distance between the input signal value and the threshold
are stored and utilized to accurately reconstruct the one-bit sampled signal.
We then utilize this information to accurately reconstruct the signal from its
one-bit samples via the randomized Kaczmarz algorithm (RKA); a strong linear
feasibility solver that selects a random linear equation at each iteration. In
the presence of noise, we employ the recent plug-and-play (PnP) priors
technique with alternating direction method of multipliers (ADMM) to exploit
integration of state-of-the-art regularizers in the reconstruction process.
Numerical experiments with RKA and PnP-ADMM-based reconstruction illustrate the
effectiveness of our proposed UNO, including its superior performance compared
to the one-bit Sigma-Delta sampling.
