Related papers: Variational Data Assimilation via Sparse Regulariz…

Data assimilation (DA) aims to estimate the full state of a dynamical system by combining partial and noisy observations with a prior model forecast, commonly referred to as the background. In atmospheric applications, this problem is…

We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms. Our key…

Sparse arrays enable resolving more direction of arrivals (DoAs) than antenna elements using non-uniform arrays. This is typically achieved by reconstructing the covariance of a virtual large uniform linear array (ULA), which is then…

Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system's time evolution. Rather than solving the…

We apply two data assimilation (DA) methods, a smoother and a filter, and a model-free machine learning (ML) shallow network to forecast two weakly turbulent systems. We analyse the effect of the spatial sparsity of observations on accuracy…

Spatial frequency estimation from a mixture of noisy sinusoids finds applications in various fields. While subspace-based methods offer cost-effective super-resolution parameter estimation, they demand precise array calibration, posing…

Recent research has shown that performance in signal processing tasks can often be significantly improved by using signal models based on sparse representations, where a signal is approximated using a small number of elements from a fixed…

Data assimilation (DA) solves the inverse problem of inferring initial conditions given data and a model. Here we use biophysically motivated Hodgkin-Huxley (HH) models of avian HVCI neurons, experimentally obtained recordings of these…

In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…

This paper is concerned with variational and Bayesian approaches to neuro-electromagnetic inverse problems (EEG and MEG). The strong indeterminacy of these problems is tackled by introducing sparsity inducing regularization/priors in a…

Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…

Data Assimilation (DA) is a methodology for combining mathematical models simulating complex systems (the background knowledge) and measurements (the reality or observational data) in order to improve the estimate of the system state. This…

Data assimilation (DA) provides a general framework for estimation in dynamical systems based on the concepts of Bayesian inference. This constitutes a common basis for the different linear and nonlinear filtering and smoothing techniques…

We show, using idealized models, that numerical data assimilation can be successful only if an effective dimension of the problem is not excessive. This effective dimension depends on the noise in the model and the data, and in physically…

Data assimilation is the process to fuse information from priors, observations of nature, and numerical models, in order to obtain best estimates of the parameters or state of a physical system of interest. Presence of large errors in some…

Sparse training reduces the memory and computational costs of deep neural networks. However, sparse optimization methods, e.g., those adding an $\ell_1$ penalty, often control sparsity only indirectly through a regularization parameter…

With the increasing penetration of high-frequency sensors across a number of biological and physical systems, the abundance of the resulting observations offers opportunities for higher statistical accuracy of down-stream estimates, but…

Regularization is a common tool in variational inverse problems to impose assumptions on the parameters of the problem. One such assumption is sparsity, which is commonly promoted using lasso and total variation-like regularization.…

We consider the inverse problem of recovering a continuous-domain function from a finite number of noisy linear measurements. The unknown signal is modeled as the sum of a slowly varying trend and a periodic or quasi-periodic seasonal…

Data assimilation (DA) plays a pivotal role in numerical weather prediction by systematically integrating sparse observations with model forecasts to estimate optimal atmospheric initial condition for forthcoming forecasts. Traditional…