Modulo sampling and dithered one-bit quantization frameworks have emerged as
promising solutions to overcome the limitations of traditional
analog-to-digital converters (ADCs) and sensors. Modulo sampling, with its
high-resolution approach utilizing modulo ADCs, offers an unlimited dynamic
range, while dithered one-bit quantization offers cost-efficiency and reduced
power consumption while operating at elevated sampling rates. Our goal is to
explore the synergies between these two techniques, leveraging their unique
advantages, and to apply them to non-bandlimited signals within spline spaces.
One noteworthy application of these signals lies in High Dynamic Range (HDR)
imaging. In this paper, we expand upon the Unlimited One-Bit (UNO) sampling
framework, initially conceived for bandlimited signals, to encompass
non-bandlimited signals found in the context of HDR imaging. We present a novel
algorithm rigorously examined for its ability to recover images from one-bit
modulo samples. Additionally, we introduce a sufficient condition specifically
designed for UNO sampling to perfectly recover non-bandlimited signals within
spline spaces. Our numerical results vividly demonstrate the effectiveness of
UNO sampling in the realm of HDR imaging.Comment: arXiv admin note: text overlap with arXiv:2308.0069