Related papers: Compressive sensing Petrov-Galerkin approximation …

Random sampling in compressive sensing (CS) enables the compression of large amounts of input signals in an efficient manner, which is useful for many applications. CS reconstructs the compressed signals exactly with overwhelming…

Sequential optimization methods are often confronted with the curse of dimensionality in high-dimensional spaces. Current approaches under the Gaussian process framework are still burdened by the computational complexity of tracking…

Compressive covariance estimation has arisen as a class of techniques whose aim is to obtain second-order statistics of stochastic processes from compressive measurements. Recently, these methods have been used in various image processing…

As computer resources become increasingly limited, traditional statistical methods face challenges in analyzing massive data, especially in functional data analysis. To address this issue, subsampling offers a viable solution by…

We propose a method to efficiently determine the optimal coarse-grained force field in mesoscopic stochastic simulations of Newtonian fluid and polymer melt systems modeled by dissipative particle dynamics (DPD) and energy conserving…

Deep generative models have become a standard for modeling priors for inverse problems, going beyond classical sparsity-based methods. However, existing theoretical guarantees are mostly confined to finite-dimensional vector spaces,…

Compressive sensing (CS) reconstructs images from sub-Nyquist measurements by solving a sparsity-regularized inverse problem. Traditional CS solvers use iterative optimizers with hand crafted sparsifiers, while early data-driven methods…

We present an efficient coresets-based neural network compression algorithm that sparsifies the parameters of a trained fully-connected neural network in a manner that provably approximates the network's output. Our approach is based on an…

Subspace learning and matrix factorization problems have great many applications in science and engineering, and efficient algorithms are critical as dataset sizes continue to grow. Many relevant problem formulations are non-convex, and in…

Bayesian inference for doubly-intractable pairwise exponential graphical models typically involves variations of the exchange algorithm or approximate Markov chain Monte Carlo (MCMC) samplers. However, existing methods for both classes of…

We develop a new compressive sensing (CS) inversion algorithm by utilizing the Gaussian mixture model (GMM). While the compressive sensing is performed globally on the entire image as implemented in our lensless camera, a low-rank GMM is…

Compressive sampling has become a widely used approach to construct polynomial chaos surrogates when the number of available simulation samples is limited. Originally, these expensive simulation samples would be obtained at random locations…

Motivated by the settings where sensing the entire tensor is infeasible, this paper proposes a novel tensor compressed sensing model, where measurements are only obtained from sensing each lateral slice via mutually independent matrices.…

Cost-efficient compressive sensing is challenging when facing large-scale data, {\em i.e.}, data with large sizes. Conventional compressive sensing methods for large-scale data will suffer from low computational efficiency and massive…

A field known as Compressive Sensing (CS) has recently emerged to help address the growing challenges of capturing and processing high-dimensional signals and data sets. CS exploits the surprising fact that the information contained in a…

In this work, a Bayesian approximate message passing algorithm is proposed for solving the multiple measurement vector (MMV) problem in compressive sensing, in which a collection of sparse signal vectors that share a common support are…

In this paper, we develop a Monte Carlo algorithm named the Frozen Gaussian Sampling (FGS) to solve the semiclassical Schr\"odinger equation based on the frozen Gaussian approximation. Due to the highly oscillatory structure of the wave…

Gaussian process (GP) regression is a non-parametric, Bayesian framework to approximate complex models. Standard GP regression can lead to an unbounded model in which some points can take infeasible values. We introduce a new GP method that…

Compressed sensing is designed to measure sparse signals directly in a compressed form. However, most signals of interest are only "approximately sparse", i.e. even though the signal contains only a small fraction of relevant (large)…

We study the compressed sensing (CS) signal estimation problem where an input signal is measured via a linear matrix multiplication under additive noise. While this setup usually assumes sparsity or compressibility in the input signal…