相关论文: An RIP-based approach to $\Sigma\Delta$ quantizati…
We investigate the sign-linear embeddings of 1-bit compressed sensing given by Gaussian measurements. One can give short arguments concerning a Restricted Isometry Property of such maps using Vapnik-Chervonenkis dimension of sparse…
Compressive sensing is a methodology for the reconstruction of sparse or compressible signals using far fewer samples than required by the Nyquist criterion. However, many of the results in compressive sensing concern random sampling…
The study of the restricted isometry property (RIP) of corrupted random matrices is particularly important in the field of compressed sensing (CS) with corruptions. If a matrix still satisfies the RIP after that a certain portion of rows…
We introduce a recursive algorithm for performing compressed sensing on streaming data. The approach consists of a) recursive encoding, where we sample the input stream via overlapping windowing and make use of the previous measurement in…
In the problem of matrix compressed sensing we aim to recover a low-rank matrix from few of its element-wise linear projections. In this contribution we analyze the asymptotic performance of a Bayes-optimal inference procedure for a model…
Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing matrix such as the restricted isometry property. Sensing matrices that satisfy this…
It is known that sparse recovery by measurements from random circulant matrices provides good recovery bounds. We generalize this to measurements that arise as a random orbit of a group representation for some finite group G. We derive…
We present herein a scheme by which to accurately evaluate the error exponents of a lossy data compression problem, which characterize average probabilities over a code ensemble of compression failure and success above or below a critical…
This paper is about iteratively reweighted basis-pursuit algorithms for compressed sensing and matrix completion problems. In a first part, we give a theoretical explanation of the fact that reweighted basis pursuit can improve a lot upon…
In Bora et al. (2017), a mathematical framework was developed for compressed sensing guarantees in the setting where the measurement matrix is Gaussian and the signal structure is the range of a generative neural network (GNN). The problem…
The Restricted Isometry Property (RIP) is a fundamental property of a matrix which enables sparse recovery. Informally, an $m \times n$ matrix satisfies RIP of order $k$ for the $\ell_p$ norm, if $\|Ax\|_p \approx \|x\|_p$ for every vector…
Existing convex relaxation-based approaches to reconstruction in compressed sensing assume that noise in the measurements is independent of the signal of interest. We consider the case of noise being linearly correlated with the signal and…
We present methods that can provide an exponential savings in the resources required to perform dynamic parameter estimation using quantum systems. The key idea is to merge classical compressive sensing techniques with quantum control…
Parallel acquisition systems are employed successfully in a variety of different sensing applications when a single sensor cannot provide enough measurements for a high-quality reconstruction. In this paper, we consider compressed sensing…
In this paper, we focus on a matrix factorization-based approach to recover low-rank {\it asymmetric} matrices from corrupted measurements. We propose an {\it Overparameterized Preconditioned Subgradient Algorithm (OPSA)} and provide, for…
We propose a class of dimension reduction methods for right censored survival data using a counting process representation of the failure process. Semiparametric estimating equations are constructed to estimate the dimension reduction…
In this paper, we compare and catalog the performance of various greedy quantized compressed sensing algorithms that reconstruct sparse signals from quantized compressed measurements. We also introduce two new greedy approaches for…
In compressed sensing one measures sparse signals directly in a compressed form via a linear transform and then reconstructs the original signal. However, it is often the case that the linear transform itself is known only approximately, a…
Compressed Sensing (CS) is an emerging field that enables reconstruction of a sparse signal $x \in {\mathbb R} ^n$ that has only $k \ll n$ non-zero coefficients from a small number $m \ll n$ of linear projections. The projections are…
The restricted isometry property (RIP) is a well-known condition that guarantees the absence of spurious local minima in low-rank matrix recovery problems with linear measurements. In this paper, we introduce a novel property named bound…