相关论文: Instance-Optimal Compressed Sensing via Posterior …

Bayesian inference with deep generative prior has received considerable interest for solving imaging inverse problems in many scientific and engineering fields. The selection of the prior distribution is learned from, and therefore an…

Optimized sensing is important for computational imaging in low-resource environments, when images must be recovered from severely limited measurements. In this paper, we propose a physics-constrained, fully differentiable, autoencoder that…

Compressed sensing (CS) provides an elegant framework for recovering sparse signals from compressed measurements. For example, CS can exploit the structure of natural images and recover an image from only a few random measurements. CS is…

We focus on Bayesian inverse problems with Gaussian likelihood, linear forward model, and priors that can be formulated as a Gaussian mixture. Such a mixture is expressed as an integral of Gaussian density functions weighted by a mixing…

In underwater acoustics, shallow water environments act as modal dispersive waveguides when considering low-frequency sources. In this context, propagating signals can be described as a sum of few modal components, each of them propagating…

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…

We introduce a deep generative framework for high-dimensional Bayesian inference that enables efficient posterior sampling. As telescopes and simulations rapidly expand the volume and resolution of astrophysical data, fast simulation-based…

We advocate an optimization procedure for variable density sampling in the context of compressed sensing. In this perspective, we introduce a minimization problem for the coherence between the sparsity and sensing bases, whose solution…

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…

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…

We study the value of information in sequential compressed sensing by characterizing the performance of sequential information guided sensing in practical scenarios when information is inaccurate. In particular, we assume the signal…

We consider a compressed sensing problem in which both the measurement and the sparsifying systems are assumed to be frames (not necessarily tight) of the underlying Hilbert space of signals, which may be finite or infinite dimensional. The…

We propose a new compressive imaging method for reconstructing 2D or 3D objects from their scattered wave-field measurements. Our method relies on a novel, nonlinear measurement model that can account for the multiple scattering phenomenon,…

We provide posterior contraction rates for constrained deep Gaussian processes in non-parametric density estimation and classication. The constraints are in the form of bounds on the values and on the derivatives of the Gaussian processes…

We derive rates of contraction of posterior distributions on nonparametric or semiparametric models based on Gaussian processes. The rate of contraction is shown to depend on the position of the true parameter relative to the reproducing…

We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix…

Distributed compressive sensing is a framework considering jointly sparsity within signal ensembles along with multiple measurement vectors (MMVs). The current theoretical bound of performance for MMVs, however, is derived to be the same…

Sampling from the posterior is a key technical problem in Bayesian statistics. Rigorous guarantees are difficult to obtain for Markov Chain Monte Carlo algorithms of common use. In this paper, we study an alternative class of algorithms…

Compressed sensing is a relatively new mathematical paradigm that shows a small number of linear measurements are enough to efficiently reconstruct a large dimensional signal under the assumption the signal is sparse. Applications for this…

We improve existing results in the field of compressed sensing and matrix completion when sampled data may be grossly corrupted. We introduce three new theorems. 1) In compressed sensing, we show that if the m \times n sensing matrix has…