Related papers: Sampling and Frequency Warping
Spherical Gauss-Laguerre (SGL) basis functions, i.e., normalized functions of the type $L_{n-l-1}^{(l + 1/2)} (r^2) r^{l} Y_{lm}(\vartheta,\varphi)$, $|m| \leq l < n \in \mathbb{N}$, $L_{n-l-1}^{(l + 1/2)}$ being a generalized Laguerre…
It is of particular interest to reconstruct or estimate bandlimited graph signals, which are smoothly varying signals defined over graphs, from partial noisy measurements. However, choosing an optimal subset of nodes to sample is NP-hard.…
Reconstruction of undersampled periodic signals of unknown period is an important signal processing operation. It is especially difficult operation when the sequences of samples are short and no information on the inter-sequence time…
Logconcave functions represent the current frontier of efficient algorithms for sampling, optimization and integration in R^n. Efficient sampling algorithms to sample according to a probability density (to which the other two problems can…
In many signal processing applications, one wishes to acquire images that are sparse in transform domains such as spatial finite differences or wavelets using frequency domain samples. For such applications, overwhelming empirical evidence…
A signature result in compressed sensing is that Gaussian random sampling achieves stable and robust recovery of sparse vectors under optimal conditions on the number of measurements. However, in the context of image reconstruction, it has…
We consider the inverse problem of reconstructing general solutions to the Helmholtz equation on some domain $\Omega$ from their values at scattered points $x_1,\dots,x_n\subset \Omega$. This problem typically arises when sampling acoustic…
We advocate an optimization procedure for variable density sampling in the context of compressed sensing. In this perspective, we introduce a minimization problem for the coherence between the sparsity and sensing bases, whose solution…
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 the recovery of multivariate functions from reproducing kernel Hilbert spaces in the uniform norm. Our main interest is to obtain preasymptotic estimates for the corresponding sampling numbers. We obtain results in terms of the…
We consider the problem of reconstructing a compactly supported function from samples of its Fourier transform taken along a spiral. We determine the Nyquist sampling rate in terms of the density of the spiral and show that below this rate…
We develop a novel sampling theorem for functions defined on the three-dimensional rotation group SO(3) by connecting the rotation group to the three-torus through a periodic extension. Our sampling theorem requires $4L^3$ samples to…
We study the problem of selecting the best sampling set for bandlimited reconstruction of signals on graphs. A frequency domain representation for graph signals can be defined using the eigenvectors and eigenvalues of variation operators…
Graph signal sampling is the problem of selecting a subset of representative graph vertices whose values can be used to interpolate missing values on the remaining graph vertices. Optimizing the choice of sampling set using concepts from…
A theoretical analysis, aimed at characterizing the degradation induced by the resampling and requantization processes applied to band-limited Gaussian signals with flat power spectrum, available through their digitized samples, is…
We propose a sampling theory for signals that are supported on either directed or undirected graphs. The theory follows the same paradigm as classical sampling theory. We show that perfect recovery is possible for graph signals bandlimited…
We derive fundamental sampling bounds for smooth signals in continuous settings without sparsity assumptions. By introducing the Fourier ratio as a measure of spectral compressibility induced by smoothness, we obtain explicit, deterministic…
The properties of the Gabor and Morlet transforms are examined with respect to the Fourier analysis of discretely sampled data. Forward and inverse transform pairs based on a fixed window with uniform sampling of the frequency axis can…
This correspondence presents an efficient method for reconstructing a band-limited signal in the discrete domain from its crossings with a sine wave. The method makes it possible to design A/D converters that only deliver the crossing…
The purpose of this paper is to introduce a very efficient algorithm for signal extrapolation. It can widely be used in many applications in image and video communication, e. g. for concealment of block errors caused by transmission errors…