[BUKU][B] Numerical fourier analysis
The Applied and Numerical Harmonic Analysis (ANHA) book series aims to provide the
engineering, mathematical, and scientific communities with significant developments in …
engineering, mathematical, and scientific communities with significant developments in …
[HTML][HTML] Sparse high-dimensional FFT based on rank-1 lattice sampling
In this paper, we suggest approximate algorithms for the reconstruction of sparse high-
dimensional trigonometric polynomials, where the support in frequency domain is unknown …
dimensional trigonometric polynomials, where the support in frequency domain is unknown …
Tight error bounds for rank-1 lattice sampling in spaces of hybrid mixed smoothness
We consider the approximate recovery of multivariate periodic functions from a discrete set
of function values taken on a rank-1 lattice. Moreover, the main result is the fact that any (non …
of function values taken on a rank-1 lattice. Moreover, the main result is the fact that any (non …
High-dimensional sparse FFT based on sampling along multiple rank-1 lattices
The reconstruction of high-dimensional sparse signals is a challenging task in a wide range
of applications. In order to deal with high-dimensional problems, efficient sparse fast Fourier …
of applications. In order to deal with high-dimensional problems, efficient sparse fast Fourier …
On the reconstruction of functions from values at subsampled quadrature points
This paper is concerned with function reconstruction from samples. The sampling points
used in several approaches are (1) structured points connected with fast algorithms or (2) …
used in several approaches are (1) structured points connected with fast algorithms or (2) …
Efficient spectral estimation by MUSIC and ESPRIT with application to sparse FFT
In spectral estimation, one has to determine all parameters of an exponential sum for finitely
many (noisy) sampled data of this exponential sum. Frequently used methods for spectral …
many (noisy) sampled data of this exponential sum. Frequently used methods for spectral …
Multiple rank-1 lattices as sampling schemes for multivariate trigonometric polynomials
L Kämmerer - Journal of Fourier Analysis and Applications, 2018 - Springer
We present a new sampling method that allows for the unique reconstruction of (sparse)
multivariate trigonometric polynomials. The crucial idea is to use several rank-1 lattices as …
multivariate trigonometric polynomials. The crucial idea is to use several rank-1 lattices as …
[HTML][HTML] Constructing spatial discretizations for sparse multivariate trigonometric polynomials that allow for a fast discrete Fourier transform
L Kämmerer - Applied and Computational Harmonic Analysis, 2019 - Elsevier
The paper discusses the construction of high dimensional spatial discretizations for arbitrary
multivariate trigonometric polynomials, where the frequency support of the trigonometric …
multivariate trigonometric polynomials, where the frequency support of the trigonometric …
[HTML][HTML] Approximation of multivariate periodic functions based on sampling along multiple rank-1 lattices
In this work, we consider the approximate reconstruction of high-dimensional periodic
functions based on sampling values. As sampling schemes, we utilize so-called …
functions based on sampling values. As sampling schemes, we utilize so-called …
Nonlinear approximation in bounded orthonormal product bases
We present a dimension-incremental algorithm for the nonlinear approximation of high-
dimensional functions in an arbitrary bounded orthonormal product basis. Our goal is to …
dimensional functions in an arbitrary bounded orthonormal product basis. Our goal is to …