Related papers: Sampling the flow of a bandlimited function
In a previous paper, the author constructed frames and oversampling formulas for band-limited functions, in the framework of the theory of shift-invariant spaces. In this article we study the problem of recovering missing samples. We find a…
Reconstructing PDE-governed fields from sparse and irregular measurements is challenging due to their ill-posed nature. Deterministic surrogates are trained on dense fields that struggle with limited measurements and uncertainty…
In numerous graph signal processing applications, data is often missing for a variety of reasons, and predicting the missing data is essential. In this paper, we consider data on graphs modeled as bandlimited graph signals. Predicting or…
In this paper, we discuss to the nonuniform sampling problem in principal shift-invariant subspaces of mixed Lebesgue spaces. We proposed a fast reconstruction algorithm which allows to exactly reconstruct the functions in the principal…
Sampling of a spatiotemporal field for environmental sensing is of interest. Traditionally, a few fixed stations or sampling locations aid in the reconstruction of the spatial field. Recently, there has been an interest in mobile sensing…
In this paper we consider the following problem of phase retrieval: Given a collection of real-valued band-limited functions $\{\psi_{\lambda}\}_{\lambda\in \Lambda}\subset L^2(\mathbb{R}^d)$ that constitutes a semi-discrete frame, we ask…
Recently efforts have been made to use generalized sinc functions to perfectly reconstruct various kinds of non-bandlimited signals. As a consequence, perfect reconstruction sampling formulas have been established using such generalized…
We show that a broad class of signal acquisition schemes can be interpreted as recording data from a signal $x$ in a space $\cal U$ (typically, though not exclusively, a space of bandlimited functions) via an orthogonal projection $w =…
We present a new turbulent data reconstruction method with supervised machine learning techniques inspired by super resolution and inbetweening, which can recover high-resolution turbulent flows from grossly coarse flow data in space and…
Inverse problems arise in a multitude of applications, where the goal is to recover a clean signal from noisy and possibly (non)linear observations. The difficulty of a reconstruction problem depends on multiple factors, such as the ground…
Many applications in computational and experimental fluid mechanics require effective methods for reconstructing the flow fields from limited sensor data. However, this task remains a significant challenge because the measurement operator,…
Band-limited functions are fundamental objects that are widely used in systems theory and signal processing. In this paper we refine a recent nonparametric, nonasymptotic method for constructing simultaneous confidence regions for…
Weighted average sampling is more practical and numerically more stable than sampling at single points as in the classical Shannon sampling framework. Using the frame theory, one can completely reconstruct a bandlimited function from its…
In this paper, we consider the problem of recovering a compactly supported multivariate function from a collection of pointwise samples of its Fourier transform taken nonuniformly. We do this by using the concept of weighted Fourier frames.…
We study spectral subspaces of the Sturm-Liouville operator $f \mapsto -(pf')'$ on $\mathbb{R}$, where $p$ is a positive, piecewise constant function. Functions in these subspaces can be thought of as having a local bandwidth determined by…
We provide conditions for exact reconstruction of a bandlimited function from irregular polar samples of its Radon transform. First, we prove that the Radon transform is a continuous L2-operator for certain classes of bandlimited signals.…
Sampling theory in fractional Fourier Transform (FrFT) domain has been studied extensively in the last decades. This interest stems from the ability of the FrFT to generalize the traditional Fourier Transform, broadening the traditional…
An inverse nonequispaced fast Fourier transform (iNFFT) is a fast algorithm to compute the Fourier coefficients of a trigonometric polynomial from nonequispaced sampling data. However, various applications such as magnetic resonance imaging…
In this paper, we consider sampling and reconstruction of signals in a reproducing kernel subspace of $L^p(\Rd), 1\le p\le \infty$, associated with an idempotent integral operator whose kernel has certain off-diagonal decay and regularity.…
Particle Image Velocimetry (PIV) systems are often limited in their ability to fully resolve the spatiotemporal fluctuations inherent in turbulent flows due to hardware constraints. In this study, we develop models based on Rapid Distortion…