Related papers: New Algorithms and Improved Guarantees for One-Bit…
Line spectral estimation is the problem of recovering the frequencies and amplitudes of a mixture of a few sinusoids from equispaced samples. However, in a variety of signal processing problems arising in imaging, radar, and localization we…
This note studies the worst-case recovery error of low-rank and bisparse matrices as a function of the number of one-bit measurements used to acquire them. First, by way of the concept of consistency width, precise estimates are given on…
Signal recovery is one of the key techniques of Compressive sensing (CS). It reconstructs the original signal from the linear sub-Nyquist measurements. Classical methods exploit the sparsity in one domain to formulate the L0 norm…
Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…
Suppose we wish to recover a signal x in C^n from m intensity measurements of the form |<x,z_i>|^2, i = 1, 2,..., m; that is, from data in which phase information is missing. We prove that if the vectors z_i are sampled independently and…
Compressed sensing (CS) is on recovery of high dimensional signals from their low dimensional linear measurements under a sparsity prior and digital quantization of the measurement data is inevitable in practical implementation of CS…
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…
Compressed sensing (CS) and 1-bit CS cannot directly recover quantized signals and require time consuming recovery. In this paper, we introduce \textit{Hamming compressed sensing} (HCS) that directly recovers a k-bit quantized signal of…
Compressed sensing deals with the recovery of sparse signals from linear measurements. Without any additional information, it is possible to recover an $s$-sparse signal using $m \gtrsim s \log(d/s)$ measurements in a robust and stable way.…
Parameterized mathematical models play a central role in understanding and design of complex information systems. However, they often cannot take into account the intricate interactions innate to such systems. On the contrary, purely…
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…
Sparse signals can be recovered from a reduced set of samples by using compressive sensing algorithms. In common methods the signal is recovered in the sparse domain. A method for the reconstruction of sparse signal which reconstructs the…
Abstract-One-bit compressive sensing (CS) is known to be particularly suited for resource-constrained wireless sensor networks (WSNs). In this paper, we consider 1-bit CS over noisy WSNs subject to channel-induced bit flipping errors, and…
To relax power consumption requirements in multigigabit/s communications systems low resolution quantization can be used. Information-theoretic results have shown that systems employing 1-bit quantization and oversampling are a viable…
In this paper we consider memoryless one-bit compressed sensing with randomly subsampled Gaussian circulant matrices. We show that in a small sparsity regime and for small enough accuracy $\delta$, $m\sim \delta^{-4} s\log(N/s\delta)$…
Signal models formed as linear combinations of few atoms from an over-complete dictionary or few frame vectors from a redundant frame have become central to many applications in high dimensional signal processing and data analysis. A core…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
In many applications we seek to recover signals from linear measurements far fewer than the ambient dimension, given the signals have exploitable structures such as sparse vectors or low rank matrices. In this paper we work in a general…
This paper formulates and studies a general distributed field reconstruction problem using a dense network of noisy one-bit randomized scalar quantizers in the presence of additive observation noise of unknown distribution. A constructive…
This letter is focused on quantized Compressed Sensing, assuming that Lasso is used for signal estimation. Leveraging recent work, we provide a framework to optimize the quantization function and show that the recovered signal converges to…