Related papers: Sampling trajectories for the short-time Fourier t…
The creation of optimal samplers can be a challenging task, especially in the presence of constraints on the support of parameters. One way of mitigating the severity of this challenge is to work with transformed variables, where the…
We study the regularity of smooth functions whose derivatives are dominated by sequences of the form $M_p^{\tau,\s}=p^{\tau p^{\s}}$, $\tau>0$, $\s\geq1$. We show that such functions can be characterized through the decay properties of…
The problem of phase retrieval, i.e., the problem of recovering a function from the magnitudes of its Fourier transform, naturally arises in various fields of physics, such as astronomy, radar, speech recognition, quantum mechanics and,…
Generalized sampling is a recently developed linear framework for sampling and reconstruction in separable Hilbert spaces. It allows one to recover any element in any finite-dimensional subspace given finitely many of its samples with…
We study the recovery of one-dimensional semipermeable barriers for a stochastic process in a planar domain. The considered process acts like Brownian motion when away from the barriers and is reflected upon contact until a sufficient but…
The theory of sampling and the reconstruction of data has a wide range of applications and a rich collection of techniques. For many methods a core problem is the estimation of the number of samples needed in order to secure a stable and…
Many reconstruction problems in signal processing require solution of a certain kind of nonlinear systems of algebraic equations, which we call Prony systems. We study these systems from a general perspective, addressing questions of global…
Some techniques for the study of intermittency by means of wavelet transforms, are presented on an example of synthetic turbulent signal. Several features of the turbulent field, that cannot be probed looking at standard structure function…
In this paper, we consider a quaternionic short-time Fourier transform (QSTFT) with normalized Hermite functions as windows. It turns out that such a transform is based on the recent theory of slice polyanalytic functions on quaternions.…
We present a computationally efficient algorithm for stable numerical differentiation from noisy, uniformly-sampled data on a bounded interval. The method combines multi-interval Fourier extension approximations with an adaptive domain…
This paper investigates the problem of dynamical sampling for graph signals influenced by a constant source term. We consider signals evolving over time according to a linear dynamical system on a graph, where both the initial state and the…
Gabor phase retrieval is the problem of reconstructing a signal from only the magnitudes of its Gabor transform. Previous findings suggest a possible link between unique solvability of the discrete problem (recovery from measurements on a…
In this paper, we show that high-dimensional sparse wavelet signals of finite levels can be constructed from their partial Fourier measurements on a deterministic sampling set with cardinality about a multiple of signal sparsity.
We study the continuity properties of trajectories for some random series of functions $\sum a\_kf(\alpha X\_k(\omega))$ where $a\_k$ is a complex sequence, $X\_k$ a sequence of real independent random variables, $f$ is a real valued…
A streamwise-constant model is presented to investigate the basic mechanisms responsible for the change in mean flow occuring during pipe flow transition. Using a single forced momentum balance equation, we show that the shape of the…
Generalized sampling consists in the recovery of a function $f$, from the samples of the responses of a collection of linear shift-invariant systems to the input $f$. The reconstructed function is typically a member of a finitely generated…
Controlled ordinary differential equations driven by continuous bounded variation curves can be considered a continuous time analogue of recurrent neural networks for the construction of expressive features of the input curves. We ask up to…
Consider the task of sampling and reconstructing a bandlimited spatial field in $\Re^2$ using moving sensors that take measurements along their path. It is inexpensive to increase the sampling rate along the paths of the sensors but more…
We introduce exact methods for the simulation of sample paths of one-dimensional diffusions with a discontinuity in the drift function. Our procedures require the simulation of finite-dimensional candidate draws from probability laws…
We introduce a new ensemble of random bipartite graphs, which we term the `smearing ensemble', where each left node is connected to some number of consecutive right nodes. Such graphs arise naturally in the recovery of sparse wavelet…