7 research outputs found
HDR Imaging With One-Bit Quantization
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
Low-rank Matrix Sensing With Dithered One-Bit Quantization
We explore the impact of coarse quantization on low-rank matrix sensing in
the extreme scenario of dithered one-bit sampling, where the high-resolution
measurements are compared with random time-varying threshold levels. To recover
the low-rank matrix of interest from the highly-quantized collected data, we
offer an enhanced randomized Kaczmarz algorithm that efficiently solves the
emerging highly-overdetermined feasibility problem. Additionally, we provide
theoretical guarantees in terms of the convergence and sample size
requirements. Our numerical results demonstrate the effectiveness of the
proposed methodology.Comment: arXiv admin note: substantial text overlap with arXiv:2308.0069
Harnessing the Power of Sample Abundance: Theoretical Guarantees and Algorithms for Accelerated One-Bit Sensing
One-bit quantization with time-varying sampling thresholds (also known as
random dithering) has recently found significant utilization potential in
statistical signal processing applications due to its relatively low power
consumption and low implementation cost. In addition to such advantages, an
attractive feature of one-bit analog-to-digital converters (ADCs) is their
superior sampling rates as compared to their conventional multi-bit
counterparts. This characteristic endows one-bit signal processing frameworks
with what one may refer to as sample abundance. We show that sample abundance
plays a pivotal role in many signal recovery and optimization problems that are
formulated as (possibly non-convex) quadratic programs with linear feasibility
constraints. Of particular interest to our work are low-rank matrix recovery
and compressed sensing applications that take advantage of one-bit
quantization. We demonstrate that the sample abundance paradigm allows for the
transformation of such problems to merely linear feasibility problems by
forming large-scale overdetermined linear systems -- thus removing the need for
handling costly optimization constraints and objectives. To make the proposed
computational cost savings achievable, we offer enhanced randomized Kaczmarz
algorithms to solve these highly overdetermined feasibility problems and
provide theoretical guarantees in terms of their convergence, sample size
requirements, and overall performance. Several numerical results are presented
to illustrate the effectiveness of the proposed methodologies.Comment: arXiv admin note: text overlap with arXiv:2301.0346
Matrix Completion via Memoryless Scalar Quantization
We delve into the impact of memoryless scalar quantization on matrix
completion. We broaden our theoretical discussion to encompass the coarse
quantization scenario with a dithering scheme, where the only available
information for low-rank matrix recovery is few-bit low-resolution data. Our
primary motivation for this research is to evaluate the recovery performance of
nuclear norm minimization in handling quantized matrix problems without the use
of any regularization terms such as those stemming from maximum likelihood
estimation. We furnish theoretical guarantees for both scenarios: when access
to dithers is available during the reconstruction process, and when we have
access solely to the statistical properties of the dithers. Additionally, we
conduct a comprehensive analysis of the effects of sign flips and
prequantization noise on the recovery performance, particularly when the impact
of sign flips is quantified using the well-known Hamming distance in the upper
bound of recovery error.Comment: arXiv admin note: substantial text overlap with arXiv:2310.0322