Related papers: Super-resolution limit of the ESPRIT algorithm
One of the main limitations for the resolution of optical instruments is the size of the sensor's pixels. In this paper we introduce a new sub pixel resolution algorithm to enhance the resolution of images. This method is based on the…
The ultimate sensitivity of optical measurements is a key element of many recent works. Classically, it is mainly limited by the shot noise limit. However, a measurement setup that incorporates quantum mechanical principles can surpass the…
A popular approach for estimating an unknown signal from noisy, linear measurements is via solving a so called \emph{regularized M-estimator}, which minimizes a weighted combination of a convex loss function and of a convex (typically,…
Discrete image registration can be a strategy to reconstruct signals from samples corrupted by blur and noise. We examine superresolution and discrete image registration for one-dimensional spatially-limited piecewise constant functions…
Spectral estimation is a fundamental task in signal processing. Recent algorithms in quantum phase estimation are concerned with the large noise, large frequency regime of the spectral estimation problem. The recent work in…
In this paper, we show that it is possible to overcome one of the fundamental limitations of super-resolution microscopy techniques: the necessity to be in an \emph{optically homogeneous} environment. Using recent modal approximation…
Denoising has to do with estimating a signal $x_0$ from its noisy observations $y=x_0+z$. In this paper, we focus on the "structured denoising problem", where the signal $x_0$ possesses a certain structure and $z$ has independent normally…
Many geometric estimation problems take the form of synchronization over the special Euclidean group: estimate the values of a set of poses given noisy measurements of a subset of their pairwise relative transforms. This problem is…
The PhaseLift algorithm is an effective convex method for solving the phase retrieval problem from Fourier measurements with coded diffraction patterns (CDP). While exact reconstruction guarantees are well-established in the noiseless case,…
Scanning Electron Microscopy (SEM) is pivotal in revealing intricate micro- and nanoscale features across various research fields. However, obtaining high-resolution SEM images presents challenges, including prolonged scanning durations and…
In this paper we study the high-dimensional super-resolution imaging problem. Here we are given an image of a number of point sources of light whose locations and intensities are unknown. The image is pixelized and is blurred by a known…
In semidefinite programming a proposed optimal solution may be quite poor in spite of having sufficiently small residual in the optimality conditions. This issue may be framed in terms of the discrepancy between forward error (the…
We establish the optimal nonergodic sublinear convergence rate of the proximal point algorithm for maximal monotone inclusion problems. First, the optimal bound is formulated by the performance estimation framework, resulting in an infinite…
We introduce a new method for Estimation of Signal Parameters based on Iterative Rational Approximation (ESPIRA) for sparse exponential sums. Our algorithm uses the AAA algorithm for rational approximation of the discrete Fourier transform…
We explore the precision with which the Einstein Telescope (ET) will be able to measure the parameters of intermediate-mass-ratio inspirals (IMRIs). We calculate the parameter estimation errors using the Fisher Matrix formalism and present…
We determine the ultimate potential of quantum imaging for boosting the resolution of a far-field, diffraction-limited, linear imaging device within the paraxial approximation. First we show that the problem of estimating the separation…
We develop an algorithm for single-image superresolution of remotely sensed data, based on the discrete shearlet transform. The shearlet transform extracts directional features of signals, and is known to provide near-optimally sparse…
A fundamental problem in statistics and machine learning is to estimate a function $f$ from possibly noisy observations of its point samples. The goal is to design a numerical algorithm to construct an approximation $\hat f$ to $f$ in a…
We demonstrate a method to obtain the spectra of $1/f$ noises in spin-qubit devices from randomized benchmarking, assisted by supervised learning. The noise exponent, which indicates the correlation within the noise, is determined by…
This paper considers fundamental limits for solving sparse inverse problems in the presence of Poisson noise with physical constraints. Such problems arise in a variety of applications, including photon-limited imaging systems based on…