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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.…
Compressed Sensing aims to capture attributes of $k$-sparse signals using very few measurements. In the standard Compressed Sensing paradigm, the $\m\times \n$ measurement matrix $\A$ is required to act as a near isometry on the set of all…
The one-bit compressed sensing framework aims to reconstruct a sparse signal by only using the sign information of its linear measurements. To compensate for the loss of scale information, past studies in the area have proposed recovering…
Distributed high dimensional mean estimation is a common aggregation routine used often in distributed optimization methods. Most of these applications call for a communication-constrained setting where vectors, whose mean is to be…
The sample complexity of estimating or maximising an unknown function in a reproducing kernel Hilbert space is known to be linked to both the effective dimension and the information gain associated with the kernel. While the information…
We consider faithfully combining phase retrieval with classical compressed sensing. Inspired by the recent novel formulation for phase retrieval called PhaseMax, we present and analyze SparsePhaseMax, a linear program for phaseless…
A new variant of the Compressed Sensing problem is investigated when the number of measurements corrupted by errors is upper bounded by some value l but there are no more restrictions on errors. We prove that in this case it is enough to…
Compressed sensing is a new scheme which shows the ability to recover sparse signal from fewer measurements, using $l_1$ minimization. Recently, Chartrand and Staneva shown in \cite{CS1} that the $l_p$ minimization with $0<p<1$ recovers…
Unlike compressive sensing where the measurement outputs are assumed to be real-valued and have infinite precision, in "one-bit compressive sensing", measurements are quantized to one bit, their signs. In this work, we show how to recover…
Given a linear system in a real or complex domain, linear regression aims to recover the model parameters from a set of observations. Recent studies in compressive sensing have successfully shown that under certain conditions, a linear…
Hoeffding's U-statistics model combinatorial-type matrix parameters (appearing in CS theory) in a natural way. This paper proposes using these statistics for analyzing random compressed sensing matrices, in the non-asymptotic regime…
We present a smooth probabilistic reformulation of $\ell_0$ regularized regression that does not require Monte Carlo sampling and allows for the computation of exact gradients, facilitating rapid convergence to local optima of the best…
We consider the optimal quantization of compressive sensing measurements following the work on generalization of relaxed belief propagation (BP) for arbitrary measurement channels. Relaxed BP is an iterative reconstruction scheme inspired…
We study the information-theoretic limits of exactly recovering the support of a sparse signal using noisy projections defined by various classes of measurement matrices. Our analysis is high-dimensional in nature, in which the number of…
We present an end-to-end image compression system based on compressive sensing. The presented system integrates the conventional scheme of compressive sampling and reconstruction with quantization and entropy coding. The compression…
In this paper we extend results taken from compressed sensing to recover Hilbert-space valued vectors. This is an important problem in parametric function approximation in particular when the number of parameters is high. By expanding our…
We propose a general measure of non-classical correlations for bipartite systems based on generalized entropic functions and majorization properties. Defined as the minimum information loss due to a local measurement, in the case of pure…
We analyze the performance of a data-assimilation algorithm based on a linear feedback control when used with observational data that contains measurement errors. Our model problem consists of dynamics governed by the two-dimension…
In this paper, we consider the problem of sparse signal detection based on partial support set estimation with compressive measurements in a distributed network. Multiple nodes in the network are assumed to observe sparse signals which…
Lossy compressors are increasingly adopted in scientific research, tackling volumes of data from experiments or parallel numerical simulations and facilitating data storage and movement. In contrast with the notion of entropy in lossless…