Related papers: Signal Recovery From 1-Bit Quantized Noisy Samples…
In this paper, we propose a general scale invariant approach for sparse signal recovery via the minimization of the $q$-ratio sparsity. When $1 < q \leq \infty$, both the theoretical analysis based on $q$-ratio constrained minimal singular…
The Compressive Sensing (CS) framework aims to ease the burden on analog-to-digital converters (ADCs) by reducing the sampling rate required to acquire and stably recover sparse signals. Practical ADCs not only sample but also quantize each…
We consider the problem of the recovery of a k-sparse vector from compressed linear measurements when data are corrupted by a quantization noise. When the number of measurements is not sufficiently large, different $k$-sparse solutions may…
In this paper, we introduce a sparse approximation property of order $s$ for a measurement matrix ${\bf A}$: $$\|{\bf x}_s\|_2\le D \|{\bf A}{\bf x}\|_2+ \beta \frac{\sigma_s({\bf x})}{\sqrt{s}} \quad {\rm for\ all} \ {\bf x},$$ where ${\bf…
A simple hard-thresholding operation is shown to be able to recover $L$ signals $\mathbf{x}_1,...,\mathbf{x}_L \in \mathbb{R}^n$ that share a common support of size $s$ from $m = \mathcal{O}(s)$ one-bit measurements per signal if $L \ge…
Quantum sensing is an emerging field with the potential to outperform classical methods in both precision and spatial resolution. However, the sensitivity of the underlying quantum platform also makes the sensors highly susceptible to their…
Frequency estimation from measurements corrupted by noise is a fundamental challenge across numerous engineering and scientific fields. Among the pivotal factors shaping the resolution capacity of any frequency estimation technique are…
Efficient all-digital post-correction of low-resolution analog-to-digital converters can be achieved by using Look-Up Tables (LUTs). The performance of a LUT can be optimized by incorporating a parametric model for the expected input…
In one-bit compressed sensing, previous results state that sparse signals may be robustly recovered when the measurements are taken using Gaussian random vectors. In contrast to standard compressed sensing, these results are not extendable…
Accurately estimating the statistical properties of noise is important in data analysis for space-based gravitational wave detectors. Noise in different time-delay interferometry channels correlates with each other. Many studies often…
We investigate design and performance of communications over the bandlimited Gaussian channel with one-bit output quantization. A transceiver structure is proposed, which generates the channel input using a finite set of time-limited and…
This paper concerns the problem of recovering an unknown but structured signal $x \in R^n$ from $m$ quadratic measurements of the form $y_r=|<a_r,x>|^2$ for $r=1,2,...,m$. We focus on the under-determined setting where the number of…
In this study, we propose a generalized turbo signal recovery algorithm to estimate a signal from quantized measurements, in which the sensing matrix is a row-orthogonal matrix, such as the partial discrete Fourier transform matrix. The…
In signal processing, several applications involve the recovery of a function given noisy modulo samples. The setting considered in this paper is that the samples corrupted by an additive Gaussian noise are wrapped due to the modulo…
In this paper, we study the missing sample recovery problem using methods based on sparse approximation. In this regard, we investigate the algorithms used for solving the inverse problem associated with the restoration of missed samples of…
Sparse signal recovery or compressed sensing can be formulated as certain sparse optimization problems. The classic optimization theory indicates that the Newton-like method often has a numerical advantage over the gradient method for…
Noise is an important factor that influences the reliability of information acquisition, transmission, processing, and storage. In order to suppress the inevitable noise effects, a fault-tolerant information processing approach via quantum…
In this paper, we study the sample complexity and develop efficient optimal algorithms for 1-bit phase retrieval: recovering a signal $\mathbf{x}\in\mathbb{R}^n$ from $m$ phaseless bits…
One-bit quantization with time-varying sampling thresholds has recently found significant utilization potential in statistical signal processing applications due to its relatively low power consumption and low implementation cost. In…
We propose a sequential quadratic programming (SQP) algorithm for inequality constrained optimization that is robust to the presence of bounded noise in function and derivative evaluations. We cover the case where constraint evaluations…