Related papers: Sampling trajectories for the short-time Fourier t…
We introduce a method to reconstruct an element of a Hilbert space in terms of an arbitrary finite collection of linearly independent reconstruction vectors, given a finite number of its samples with respect to any Riesz basis. As we…
Reconstructing a finite set of curves from an unordered set of sample points is a well studied topic. There has been less effort that considers how much better the reconstruction can be if tangential information is given as well. We show…
We develop a framework for efficient streaming reconstructions of turbulent velocity fluctuations from limited sensor measurements with the goal of enabling real-time applications. The reconstruction process is simplified by computing…
The machine learning random Fourier feature method for data in high dimension is computationally and theoretically attractive since the optimization is based on a convex standard least squares problem and independent sampling of Fourier…
A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this…
We investigate the uniqueness of short-time Fourier transform phase retrieval problems in $L^2(\mathbb{R})$. In particular, for underlying window functions whose Fourier transform decay faster than any exponential function, we derive…
In this paper we investigate new results on the theory of superoscillations using time-frequency analysis tools and techniques such as the short-time Fourier transform (STFT) and the Zak transform. We start by studying how the short-time…
We study the design of sampling trajectories for stable sampling and the reconstruction of bandlimited spatial fields using mobile sensors. The spectrum is assumed to be a symmetric convex set. As a performance metric we use the path…
Short-time Fourier transform (STFT) phase retrieval refers to the reconstruction of a function $f$ from its spectrogram, i.e., the magnitudes of its short-time Fourier transform $V_gf$ with window function $g$. While it is known that for…
The reconstruction of unsteady flow fields from limited measurements is a challenging and crucial task for many engineering applications. Machine learning models are gaining popularity for solving this problem due to their ability to learn…
We introduce a path sampling method for obtaining statistical properties of an arbitrary stochastic dynamics. The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, modifying…
This paper presents some results on a well-known problem in Algebraic Signal Sampling and in other areas of applied mathematics: reconstruction of piecewise-smooth functions from their integral measurements (like moments, Fourier…
Finite-rate-of-innovation (FRI) signals are ubiquitous in applications such as radar, ultrasound, and time of flight imaging. Due to their finite degrees of freedom, FRI signals can be sampled at sub-Nyquist rates using appropriate sampling…
Fourier methods have a long and proven track record as an excellent tool in data processing. As memory and computational constraints gain importance in embedded and mobile applications, we propose to combine Fourier methods and recurrent…
We consider sampling strategies for a class of multivariate bandlimited functions $f$ that have a spectrum consisting of disjoint frequency bands. Taking advantage of the special spectral structure, we provide formulas relating $f$ to the…
We analyze signal recovery when samples are taken concomitantly from a signal and its Fourier transform. This two-sided sampling framework extends classical one-sided reconstruction and is particularly useful when measurements in either…
Phase retrieval from phaseless short-time Fourier transform (STFT) measurements is known to be inherently unstable when measurements are taken with respect to a single window. While an explicit inversion formula exists, it is useless in…
A short sample sequence of a finite-length pulse signal allows for its reconstruction only if the signal has a sparse representation in some basis. The recurrence of the pulse allows for a statistical approach to its reconstruction. We…
Single cell responses are shaped by the geometry of signaling kinetic trajectories carved in a multidimensional space spanned by signaling protein abundances. It is however challenging to assay large number (>3) of signaling species in…
We revisit the classical problem of Fourier-sparse signal reconstruction -- a variant of the \emph{Set Query} problem -- which asks to efficiently reconstruct (a subset of) a $d$-dimensional Fourier-sparse signal ($\|\hat{x}(t)\|_0 \leq…