Related papers: Sampling the flow of a bandlimited function
We consider the recovery of real-valued bandlimited functions from the absolute values of their samples, possibly spaced nonuniformly. We show that such a reconstruction is always possible if the function is sampled at more than twice its…
We consider the problem of recovering a compactly-supported function from a finite collection of pointwise samples of its Fourier transform taking nonuniformly. First, we show that under suitable conditions on the sampling frequencies -…
In this work, we investigate the sampling and reconstruction of spectrally $s$-sparse bandlimited graph signals governed by heat diffusion processes. We propose a random space-time sampling regime, referred to as {randomized} dynamical…
We consider the problem of random sampling for band-limited functions. When can a band-limited function $f$ be recovered from randomly chosen samples $f(x_j), j\in \mathbb{N}$? We estimate the probability that a sampling inequality of the…
We study the problem of recovering an unknown compactly-supported multivariate function from samples of its Fourier transform that are acquired nonuniformly, i.e. not necessarily on a uniform Cartesian grid. Reconstruction problems of this…
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 study the problem of stable reconstruction of the short-time Fourier transform from samples taken from trajectories in $\R^2$. We first consider the interplay between relative density of the trajectory and the reconstruction property.…
Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a nonlinear shrinking of…
In this paper we study the reconstruction of a bandlimited signal from samples generated by the integrate and fire model. This sampler allows us to trade complexity in the reconstruction algorithms for simple hardware implementations, and…
We propose an adaptive non-uniform sampling framework for bandlimited signals based on an algorithm-encoder co-design perspective. By revisiting the convergence analysis of iterative reconstruction algorithms for non-uniform measurements,…
For a wide family of even kernels $\{\varphi_u, u\in I\}$, we describe discrete sets $\Lambda$ such that every bandlimited signal $f$ can be reconstructed from the space-time samples $\{(f\ast\varphi_u)(\lambda), \lambda\in\Lambda, u\in…
Heat diffusion processes have found wide applications in modelling dynamical systems over graphs. In this paper, we consider the recovery of a $k$-bandlimited graph signal that is an initial signal of a heat diffusion process from its…
This paper studies several aspects of signal reconstruction of sampled data in spaces of bandlimited functions. In the first part, signal spaces are characterized in which the classical sampling series uniformly converge, and we investigate…
We study phaseless sampling in spline spaces generated by B-splines with arbitrary knots. For real spline spaces, we give a necessary and sufficient condition for a sequence of sampling points to admit a local phase retrieval of any…
Phaseless reconstruction from space-time samples is a nonlinear problem of recovering a function $x$ in a Hilbert space $\mathcal{H}$ from the modulus of linear measurements $\{\lvert \langle x, \phi_i\rangle \rvert$, $ \ldots$, $\lvert…
We give an overview of recent developments in the problem of reconstructing a band-limited signal from non-uniform sampling from a numerical analysis view point. It is shown that the appropriate design of the finite-dimensional model plays…
In this paper we analyze two-dimensional wavelet reconstructions from Fourier samples within the framework of generalized sampling. For this, we consider both separable compactly-supported wavelets and boundary wavelets. We prove that the…
We discuss the problems of uniqueness, sampling and reconstruction with derivatives in the space of bandlimited functions. We prove that if X is sequence of real numbers such that the maximum gap between two consecutive samples is less than…
We consider inverse problems consisting of the reconstruction of an unknown signal $f$ from noisy measurements $y=Ff+\text{noise}$, where $Ff$ is a function on a Riemannian manifold without boundary $\mathcal M$. We consider the case when…
Contrary to the traditional pursuit of research on nonuniform sampling of bandlimited signals, the objective of the present paper is not to find sampling conditions that permit perfect reconstruction, but to perform the best possible signal…