Related papers: Bounds on restricted isometry constants of random …
Compressed sensing (CS) is a signal acquisition paradigm to simultaneously acquire and reduce dimension of signals that admit sparse representation. This is achieved by collecting linear, non-adaptive measurements of a signal, which can be…
This paper deals with the problem of robust matrix completion -- retrieving a low-rank matrix and a sparse matrix from the compressed counterpart of their superposition. Though seemingly not an unresolved issue, we point out that the…
The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an…
Quantum entanglement is a useful resource for implementing communication tasks. However, for the resource to be useful in practice, it needs to be accessible by parties with bounded computational resources. Computational entanglement…
Restricted Boltzmann machine (RBM) provide a general framework for modeling physical systems, but their behavior is dependent on hyperparameters such as the learning rate, the number of hidden nodes and the form of the threshold function.…
The spectra of random feature matrices provide essential information on the conditioning of the linear system used in random feature regression problems and are thus connected to the consistency and generalization of random feature models.…
The purpose of this thesis is to develop new theories on high-dimensional structured signal recovery under a rather weak assumption on the measurements that only a finite number of moments exists. High-dimensional recovery has been one of…
In [8] the author of this paper continued the research on the complex-valued discrete random variables $X_l(m,N)$ ($0\le l\le N-1$, $1\le M\le N)$ recently introduced and studied in [24]. Here we extend our results by considering $X_l(m,N)$…
In this paper, we provide a new approach to estimating the error of reconstruction from $\Sigma\Delta$ quantized compressed sensing measurements. Our method is based on the restricted isometry property (RIP) of a certain projection of the…
This study aims at contributing to lower bounds for empirical compatibility constants or empirical restricted eigenvalues. This is of importance in compressed sensing and theory for $\ell_1$-regularized estimators. Let $X$ be an $n \times…
Compressive sensing has been receiving a great deal of interest from researchers in many areas because of its ability in speeding up data acquisition. This framework allows fast signal acquisition and compression when signals are sparse in…
This paper presents a novel parametric scattering model (PSM) for sensing extended targets in integrated sensing and communication (ISAC) systems. The PSM addresses the limitations of traditional models by efficiently capturing the target's…
In Compressive Sensing, the Restricted Isometry Property (RIP) ensures that robust recovery of sparse vectors is possible from noisy, undersampled measurements via computationally tractable algorithms. It is by now well-known that Gaussian…
In the context of compressed sensing (CS), both Subspace Pursuit (SP) and Compressive Sampling Matching Pursuit (CoSaMP) are very important iterative greedy recovery algorithms which could reduce the recovery complexity greatly comparing…
We derive Concentration of Measure (CoM) inequalities for randomized Toeplitz matrices. These inequalities show that the norm of a high-dimensional signal mapped by a Toeplitz matrix to a low-dimensional space concentrates around its mean…
This paper studies the estimation and inference for the isotonic regression at the boundary point, an object that is particularly interesting and required in the analysis of monotone regression discontinuity designs. We show that the…
Optical systems which measure independent random projections of a scene according to compressed sensing (CS) theory face a myriad of practical challenges related to the size of the physical platform, photon efficiency, the need for high…
This paper proposes a reduced-rank scheme for adaptive beamforming based on the constrained joint iterative optimization of filters. We employ this scheme to devise two novel reduced-rank adaptive algorithms according to the constant…
This paper presents several novel theoretical results regarding the recovery of a low-rank matrix from just a few measurements consisting of linear combinations of the matrix entries. We show that properly constrained nuclear-norm…
The problem of estimating the frequencies of an exponential sum has been studied extensively over the last years. It can be understood as a sparse estimation problem, as it strives to identify the sparse representation of a signal using…