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Scalar quantization is the most practical and straightforward approach to signal quantization. However, it has been shown that scalar quantization of oversampled or Compressively Sensed signals can be inefficient in terms of the…
Quantization is an essential step in digitizing signals, and, therefore, an indispensable component of any modern acquisition system. This book chapter explores the interaction of quantization and compressive sensing and examines practical…
The latest theoretical advances in the field of unlimited sampling framework (USF) show the potential to avoid clipping problems of analog-to-digital converters (ADC). To date, most of the related works have focused on real-valued modulo…
We derive fundamental lower bounds on the performance of optical metrology and communication systems in a Bayesian framework. The derivation uses classical rate-distortion theory in conjunction with bounds on the capacity to transmit…
This paper provides statistical guarantees on the accuracy of dynamical models learned from dependent data sequences. Specifically, we develop uniform error bounds that apply to quantized models and imperfect optimization algorithms…
Sampling above the Nyquist rate is at the heart of sigma-delta modulation, where the increase in sampling rate is translated to a reduction in the overall (mean-squared-error) reconstruction distortion. This is attained by using a feedback…
In this paper, we study the performance of the PCM scheme with linear quantization rule for quantizing finite unit-norm tight frame expansions for $\R^d$ and derive the PCM quantization error without the White Noise Hypothesis. We prove…
Numerical multiscale methods usually rely on some coupling between a macroscopic and a microscopic model. The macroscopic model is incomplete as effective quantities, such as the homogenized material coefficients or fluxes, are missing in…
This paper provides new error bounds on "consistent" reconstruction methods for signals observed from quantized random projections. Those signal estimation techniques guarantee a perfect matching between the available quantized data and a…
Using combinatorial arguments, we determine an upper bound on achievable rates of stabilizer codes used over the quantum erasure channel. This allows us to recover the no-cloning bound on the capacity of the quantum erasure channel, R is…
This paper considers the context of multiuser massive MIMO downlink precoding with low-resolution digital-to-analog converters (DACs) at the transmitter. This subject is motivated by the consideration that it is expensive to employ…
There have been a number of studies on sparse signal recovery from one-bit quantized measurements. Nevertheless, little attention has been paid to the choice of the quantization thresholds and its impact on the signal recovery performance.…
Evaluating the statistical dimension is a common tool to determine the asymptotic phase transition in compressed sensing problems with Gaussian ensemble. Unfortunately, the exact evaluation of the statistical dimension is very difficult and…
We construct high order low-bit Sigma-Delta $(\Sigma \Delta)$ quantizers for the vector-valued setting of fusion frames. We prove that these $\Sigma \Delta$ quantizers can be stably implemented to quantize fusion frame measurements on…
In this paper we investigate encoding the bit-stream resulting from coarse Sigma-Delta quantization of finite frame expansions (i.e., overdetermined representations) of vectors. We show that for a wide range of finite-frames, including…
We show that the method of distributed noise-shaping beta-quantization offers superior performance for the problem of spectral super-resolution with quantization whenever there is redundancy in the number of measurements. More precisely, if…
It is known that the estimated energy consumption of digital-to analog converters (DACs) is around 30\% of the energy consumed by analog-to-digital converters (ADCs) keeping fixed the sampling rate and bit resolution. Assuming that…
In a networked control system, quantization is inevitable to transmit control and measurement signals. While uniform quantizers are often used in practical systems, the overloading, which is due to the limitation on the number of bits in…
In this work, the problem of signal parameter estimation from measurements acquired by a low-complexity analog-to-digital converter (ADC) with $1$-bit output resolution and an unknown quantization threshold is considered. Single-comparator…
Given a set of samples, a few of them being possibly saturated, we propose an efficient algorithm in order to cancel saturation while reconstructing band-limited signals. Our method satisfies a minimum-loss constraint and relies on…