Related papers: Spectral Factorization, Whitening- and Estimation …
Double Exponential Smoothing (DES) has broad application in various fields primarily as a forecasting tool. The values of the two smoothing parameters and , involved in DES, are traditionally chosen by the users which yield minimum MSE. In…
Vignetting in camera lenses is generally seen as something to avoid. For spectral cameras with thin-film interference filters, however, we argue that vignetting can be an advantage. When illuminated by focused light, the bandwidth of…
The Wiener Filter (WF) technique enables the reconstruction of density and velocity fields from observed radial peculiar velocities. This paper aims at identifying the optimal design of peculiar velocity surveys within the WF framework. The…
This work presents a unified framework for defining a family of noise reduction techniques for speech enhancement applications. The proposed approach provides a unique theoretical foundation for some widely-applied soft and hard…
The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…
We present a simple nonlinear digital pre-distortion (DPD) of optical transmitter components, which consists of concatenated blocks of a finite impulse response (FIR) filter, a memoryless nonlinear function and another FIR filter. The model…
This paper addresses two interrelated problems of the nonlinear filtering mechanism and fast attitude filtering with the matrix Fisher distribution (MFD) on the special orthogonal group. By analyzing the distribution evolution along Bayes'…
Data assimilation methodologies are designed to incorporate noisy observations of a physical system into an underlying model in order to infer the properties of the state of the system. Filters refer to a class of data assimilation…
Measurements of the scalar dissipation rate are performed in an impulsively started gas jet, using planar laser induced fluorescence. The measurements are well resolved spatially. The deteriorating effect of experimental noise on this…
This paper describes various approaches to modeling a random process with a given rational power spectral density. The main attention is paid to the spectral form of mathematical description, which allows one to obtain a relation for the…
Measuring a weak force is an important task for micro-mechanical systems, both when using devices as sensitive detectors and, particularly, in experiments of quantum mechanics. The optimal strategy for resolving a weak stochastic signal…
The dynamics of many open quantum systems are described by stochastic master equations. In the discrete-time case, we recall the structure of the derived quantum filter governing the evolution of the density operator conditioned to the…
The problem of image restoration in cryo-EM entails correcting for the effects of the Contrast Transfer Function (CTF) and noise. Popular methods for image restoration include `phase flipping', which corrects only for the Fourier phases but…
Self-heterodyne beat note measurements are widely used for the experimental characterization of the frequency noise power spectral density (FN-PSD) and the spectral linewidth of lasers. The measured data, however, must be corrected for the…
We discuss the rigorous justification of the spatial discretization by means of Fourier spectral methods of quasilinear first-order hyperbolic systems. We provide uniform stability estimates that grant spectral convergence of the…
We consider statistical models where functional data are artificially contaminated by independent Wiener processes in order to satisfy privacy constraints. We show that the corrupted observations have a Wiener density which determines the…
Using waves to explore our environment is a widely used paradigm, ranging from seismology to radar technology, and from bio-medical imaging to precision measurements. In all of these fields, the central aim is to gather as much information…
We study an estimator for smoothing irregularly sampled data into a smooth map. The estimator has been widely used in astronomy, owing to its low level of noise; it involves a weight function -- or smoothing kernel -- w(\theta). We show…
Let $(\Omega,\mathcal{F},(\mathcal{F}_t)_{t \geq 0},\mathbb{P})$ be a filtered probability space satisfying the usual assumptions: it is usually not possible to extend to $\mathcal{F}_{\infty}$ (the $\sigma$-algebra generated by…
The problem of stability of the optimal filter is revisited. The optimal filter (or filtering process) is the conditional probability of the current state of some stochastic process (the signal process), given both present and past values…