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In this article, we introduce and analyze a deep learning based approximation algorithm for SPDEs. Our approach employs neural networks to approximate the solutions of SPDEs along given realizations of the driving noise process. If applied…

Many signal processing applications require estimation of time-varying sparse signals, potentially with the knowledge of an imperfect dynamics model. In this paper, we propose an algorithm for dynamic filtering of time-varying sparse…

Bayesian change-point detection, together with latent variable models, allows to perform segmentation over high-dimensional time-series. We assume that change-points lie on a lower-dimensional manifold where we aim to infer subsets of…

Detection of level shifts in a noisy signal, or trend break detection, is a problem that appears in several research fields, from biophysics to optics and economics. Although many algorithms have been developed to deal with such problem,…

Cross-correlation heterodyne detectors exhibit the potential for suppression of the detection quantum noise below shot noise without use of optical squeezing for capturing weak optical signals in low frequency bands. To understand the…

We consider a multi-object detection problem over a sensor network (SNET) with limited range multi-modal sensors. Limited range sensing environment arises in a sensing field prone to signal attenuation and path losses. The general problem…

Recently, many new challenges in Compressed Sensing (CS), such as block sparsity, arose. In this paper, we present a new algorithm for solving CS with block sparse constraints (BSC) in complex fields. Firstly, based on block sparsity…

We assume the direct sum <A> o <B> for the signal subspace. As a result of post- measurement, a number of operational contexts presuppose the a priori knowledge of the LB -dimensional "interfering" subspace <B> and the goal is to estimate…

We present a statistical learning framework for robust identification of partial differential equations from noisy spatiotemporal data. Extending previous sparse regression approaches for inferring PDE models from simulated data, we address…

Sparse Bayesian learning (SBL) is a popular approach to sparse signal recovery in compressed sensing (CS). In SBL, the signal sparsity information is exploited by assuming a sparsity-inducing prior for the signal that is then estimated…

In conventional approaches for multiobject tracking (MOT), raw sensor data undergoes several preprocessing stages to reduce data rate and computational complexity. This typically includes coherent processing that aims at maximizing the…

This paper proposes an adaptive sparse polynomial chaos expansion(PCE)-based method to quantify the impacts of uncertainties on critical clearing time (CCT) that is an important index in transient stability analysis. The proposed method can…

We consider the problem of mixed sparse linear regression with two components, where two real $k$-sparse signals $\beta_1, \beta_2$ are to be recovered from $n$ unlabelled noisy linear measurements. The sparsity is allowed to be sublinear…

Seismic data noise processing is an important part of seismic exploration data processing, and the effect of noise elimination is directly related to the follow-up processing of data. In response to this problem, many authors have proposed…

Hyperspectral salient object detection (HSOD) aims to extract targets or regions with significantly different spectra from hyperspectral images. While existing deep learning-based methods can achieve good detection results, they generally…

The Sparse Vector Technique (SVT) is one of the most fundamental tools in differential privacy (DP). It works as a backbone for adaptive data analysis by answering a sequence of queries on a given dataset, and gleaning useful information in…

In this paper, the sparse sensor placement problem for least-squares estimation is considered, and the previous novel approach of the sparse sensor selection algorithm is extended. The maximization of the determinant of the matrix which…

The widespread use of machine learning algorithms calls for automatic change detection algorithms to monitor their behavior over time. As a machine learning algorithm learns from a continuous, possibly evolving, stream of data, it is…

Sparse model identification enables nonlinear dynamical system discovery from data. However, the control of false discoveries for sparse model identification is challenging, especially in the low-data and high-noise limit. In this paper, we…

Bayesian Knowledge Tracing (BKT) is a widely used and interpretable student modeling approach in intelligent tutoring systems and educational data mining. However, most implementations rely on expectation-maximization or related…