相关论文: Almost Lossless Analog Signal Separation
We study the problem of approximately recovering signals on a manifold from one-bit linear measurements drawn from either a Gaussian ensemble, partial circulant ensemble, or bounded orthonormal ensemble and quantized using Sigma-Delta or…
Affine phase retrieval is the problem of recovering signals from the magnitude-only measurements with a priori information. In this paper, we use the $\ell_1$ minimization to exploit the sparsity of signals for affine phase retrieval,…
In many data acquisition systems it is common to observe signals whose amplitudes have been clipped. We present two new algorithms for recovering a clipped signal by leveraging the model assumption that the underlying signal is sparse in…
In the context of compressed sensing (CS), this paper considers the problem of reconstructing sparse signals with the aid of other given correlated sources as multiple side information. To address this problem, we theoretically study a…
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…
Approximate message passing (AMP) methods have gained recent traction in sparse signal recovery. Additional information about the signal, or \emph{side information} (SI), is commonly available and can aid in efficient signal recovery. This…
We propose the notion of a sample distortion (SD) function for independent and identically distributed (i.i.d) compressive distributions to fundamentally quantify the achievable reconstruction performance of compressed sensing for certain…
This paper introduces a simple and very general theory of compressive sensing. In this theory, the sensing mechanism simply selects sensing vectors independently at random from a probability distribution F; it includes all models - e.g.…
The problem of minimization of the number of measurements needed for digital image acquisition and reconstruction with a given accuracy is addressed. Basics of the sampling theory are outlined to show that the lower bound of signal sampling…
This paper considers the noisy sparse phase retrieval problem: recovering a sparse signal $x \in \mathbb{R}^p$ from noisy quadratic measurements $y_j = (a_j' x )^2 + \epsilon_j$, $j=1, \ldots, m$, with independent sub-exponential noise…
This work considers distributed sensing and transmission of sporadic random samples. Lower bounds are derived for the reconstruction error of a single normally or uniformly-distributed finite-dimensional vector imperfectly measured by a…
Infinite-dimensional compressed sensing deals with the recovery of analog signals (functions) from linear measurements, often in the form of integral transforms such as the Fourier transform. This framework is well-suited to many real-world…
We address the problem of recovering signals from samples taken at their rate of innovation. Our only assumption is that the sampling system is such that the parameters defining the signal can be stably determined from the samples, a…
Tight bounds for several symmetric divergence measures are derived in terms of the total variation distance. It is shown that each of these bounds is attained by a pair of 2 or 3-element probability distributions. An application of these…
We investigate conditions for the unique recoverability of sparse integer-valued signals from a small number of linear measurements. Both the objective of minimizing the number of nonzero components, the so-called $\ell_0$-norm, as well as…
We study the image retrieval problem at the wireless edge, where an edge device captures an image, which is then used to retrieve similar images from an edge server. These can be images of the same person or a vehicle taken from other…
With the advent of massive data outputs at a regular rate, admittedly, signal processing technology plays an increasingly key role. Nowadays, signals are not merely restricted to physical sources, they have been extended to digital sources…
Phase retrieval refers to a classical nonconvex problem of recovering a signal from its Fourier magnitude measurements. Inspired by the compressed sensing technique, signal sparsity is exploited in recent studies of phase retrieval to…
Sparse signal recovery has been a cornerstone of advancements in data processing and imaging. Recently, the squared ratio of $\ell_1$ to $\ell_2$ norms, $(\ell_1/\ell_2)^2$, has been introduced as a sparsity-prompting function, showing…
We describe a method for lossless quantum compression if the output of the information source is not known. We compute the best possible compression rate, minimizing the expected base length of the output quantum bit string (the base length…