Super-resolution limit of the ESPRIT algorithm
The problem of imaging point objects can be formulated as estimation of an unknown atomic
measure from its M+ 1 consecutive noisy Fourier coefficients. The standard resolution of this …
measure from its M+ 1 consecutive noisy Fourier coefficients. The standard resolution of this …
Stable super-resolution limit and smallest singular value of restricted Fourier matrices
We consider the inverse problem of recovering the locations and amplitudes of a collection
of point sources represented as a discrete measure, given M+ 1 of its noisy low-frequency …
of point sources represented as a discrete measure, given M+ 1 of its noisy low-frequency …
Conditioning of partial nonuniform Fourier matrices with clustered nodes
We prove sharp lower bounds for the smallest singular value of a partial Fourier matrix with
arbitrary" off the grid" nodes (equivalently, a rectangular Vandermonde matrix with the nodes …
arbitrary" off the grid" nodes (equivalently, a rectangular Vandermonde matrix with the nodes …
Computational resolution in single molecule localization–impact of noise level and emitter density
M Hockmann, S Kunis, R Kurre - Biological Chemistry, 2023 - degruyter.com
Classical fluorescence microscopy is a powerful technique to image biological specimen
under close-to-native conditions, but light diffraction limits its optical resolution to 200–300 …
under close-to-native conditions, but light diffraction limits its optical resolution to 200–300 …
Improved resolution estimate for the two-dimensional super-resolution and a new algorithm for direction of arrival estimation with uniform rectangular array
In this paper, we develop a new technique to obtain improved estimates for the
computational resolution limits in two-dimensional super-resolution problems and present a …
computational resolution limits in two-dimensional super-resolution problems and present a …
A mathematical theory of computational resolution limit in multi-dimensional spaces
Resolving a linear combination of point sources from their Fourier data in a bounded domain
is a fundamental problem in imaging and signal processing. With incomplete Fourier data …
is a fundamental problem in imaging and signal processing. With incomplete Fourier data …
A theory of computational resolution limit for line spectral estimation
Line spectral estimation is a classical signal processing problem that aims to estimate the
line spectra from their signal which is contaminated by deterministic or random noise …
line spectra from their signal which is contaminated by deterministic or random noise …
[HTML][HTML] The spectral properties of Vandermonde matrices with clustered nodes
D Batenkov, B Diederichs, G Goldman… - Linear Algebra and its …, 2021 - Elsevier
We study rectangular Vandermonde matrices V with N+ 1 rows and s irregularly spaced
nodes on the unit circle, in cases where some of the nodes are “clustered” together–the …
nodes on the unit circle, in cases where some of the nodes are “clustered” together–the …
On the stable resolution limit of total variation regularization for spike deconvolution
MF Da Costa, Y Chi - IEEE Transactions on Information Theory, 2020 - ieeexplore.ieee.org
The stability of spike deconvolution, which aims at recovering point sources from their
convolution with a point spread function (PSF), is known to be related to the separation …
convolution with a point spread function (PSF), is known to be related to the separation …
On the stability of super-resolution and a Beurling–Selberg type extremal problem
MF Da Costa, U Mitra - 2022 IEEE International Symposium on …, 2022 - ieeexplore.ieee.org
Super-resolution estimation is the problem of recovering a stream of spikes (point sources)
from the noisy observation of a few numbers of its first trigonometric moments. The …
from the noisy observation of a few numbers of its first trigonometric moments. The …