Related papers: Data-driven Algorithms for signal processing with …

Conservation laws are an inherent feature in many systems modeling real world phenomena, in particular, those modeling biological and chemical systems. If the form of the underlying dynamical system is known, linear algebra and algebraic…

This paper presents a novel data-driven, direct filtering approach for unknown linear time-invariant systems affected by unknown-but-bounded measurement noise. The proposed technique combines independent multistep prediction models,…

For the solution of full-rank ill-posed linear systems a new approach based on the Arnoldi algorithm is presented. Working with regularized systems, the method theoretically reconstructs the true solution by means of the computation of a…

While filtered back projection (FBP) is still the method of choice for fast tomographic reconstruction, its performance degrades noticeably in the presence of noise, incomplete sampling, or non-standard scan geometries. We propose a…

The modern machine learning methods allow one to obtain the data-driven models in various ways. However, the more complex the model is, the harder it is to interpret. In the paper, we describe the algorithm for the mathematical equations…

Optimization-based problems have become of great interest for signal approximation purposes, as they achieved good accuracy results while being extremely flexible and versatile. In this work, we put our focus on the context of periodic…

We propose an algorithm to impute and forecast a time series by transforming the observed time series into a matrix, utilizing matrix estimation to recover missing values and de-noise observed entries, and performing linear regression to…

Systems of Prony type appear in various signal reconstruction problems such as finite rate of innovation, superresolution and Fourier inversion of piecewise smooth functions. We propose a novel approach for solving Prony-type systems, which…

The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and…

We consider the frequency estimation of periodic signals using noisy time-of-arrival (TOA) information with missing (sparse) data contaminated with outliers. We tackle the problem from a mathematical optimization standpoint, formulating it…

This paper introduces a new series of methods which combine modal decomposition algorithms, such as singular value decomposition and high-order singular value decomposition, and deep learning architectures to repair, enhance, and increase…

We present a flexible data-driven method for dynamical system analysis that does not require explicit model discovery. The method is rooted in well-established techniques for approximating the Koopman operator from data and is implemented…

The extraction of geoelectric structural information from airborne transient electromagnetic(ATEM)data primarily involves data processing and inversion. Conventional methods rely on empirical parameter selection, making it difficult to…

Medical ultrasound imaging relies heavily on high-quality signal processing to provide reliable and interpretable image reconstructions. Conventionally, reconstruction algorithms where derived from physical principles. These algorithms rely…

This work introduces the concept of parametric Gaussian processes (PGPs), which is built upon the seemingly self-contradictory idea of making Gaussian processes parametric. Parametric Gaussian processes, by construction, are designed to…

We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the…

Data values in a dataset can be missing or anomalous due to mishandling or human error. Analysing data with missing values can create bias and affect the inferences. Several analysis methods, such as principle components analysis or…

We present effective numerical algorithms for locally recovering unknown governing differential equations from measurement data. We employ a set of standard basis functions, e.g., polynomials, to approximate the governing equation with high…

We present a numerical framework for recovering unknown non-autonomous dynamical systems with time-dependent inputs. To circumvent the difficulty presented by the non-autonomous nature of the system, our method transforms the solution state…

We give the first polynomial-time algorithm for performing linear or polynomial regression resilient to adversarial corruptions in both examples and labels. Given a sufficiently large (polynomial-size) training set drawn i.i.d. from…