Related papers: On the Stable Resolution Limit of Total Variation …
Two-point super-resolution is an important problem in many signal processing applications. In this paper, we aim to establish a resolution theory for two-point super-resolution from a single snapshot. We consider a complex two-point model…
Achieving resolution in the sub-Rayleigh regime (superresolution) is one of the rapidly developing topics in quantum optics and metrology. Recently, it was shown that perfect measurement based on spatial mode demultiplexing (SPADE) in…
This paper focuses on the fundamental aspects of super-resolution, particularly addressing the stability of super-resolution and the estimation of two-point resolution. Our first major contribution is the introduction of two…
Point-spread function (PSF) estimation in spatially undersampled images is challenging because large pixels average fine-scale spatial information. This is problematic when fine-resolution details are necessary, as in optimal photometry…
We consider the problem of estimating the spatial separation between two mutually incoherent point light sources using the super-resolution imaging technique based on spatial mode demultiplexing with noisy detectors. We show that in the…
In this work we derive analytic expressions and numerical recipes for finding the effective observed position of sources close enough on sky that their Point Spread Functions (PSF), modelled as Gaussian profiles, overlap. In particularly we…
Ultrasound is widely used in medical diagnostics allowing for accessible and powerful imaging but suffers from resolution limitations due to diffraction and the finite aperture of the imaging system, which restricts diagnostic use. The…
This paper studies sparse super-resolution in arbitrary dimensions. More precisely, it develops a theoretical analysis of support recovery for the so-called BLASSO method, which is an off-the-grid generalisation of l1 regularization (also…
The spatial resolution of astronomical images is limited by atmospheric turbulence and diffraction in the telescope optics, resulting in blurred images. This makes it difficult to accurately measure the brightness of blended objects because…
Sparse regularization is a central technique for both machine learning (to achieve supervised features selection or unsupervised mixture learning) and imaging sciences (to achieve super-resolution). Existing performance guaranties assume a…
This paper studies the spectral estimation problem of estimating the locations of a fixed number of point sources given multiple snapshots of Fourier measurements collected by a uniform array of sensors. We prove novel stability bounds for…
We propose a new point-spread function (PSF) deconvolution algorithm for images of galaxies hosting an active galactic nucleus (AGN), designed to simultaneously enhance the spatial resolution of the host galaxy and remove the bright central…
It is well-known that point sources with sufficient mutual distance can be reconstructed exactly from finitely many Fourier measurements by solving a convex optimization problem with Tikhonov-regularization (this property is sometimes…
Spatial mode demultiplexing was proved to be a successful tool for estimation of the separation between incoherent sources, allowing for sensitivity much below the Rayleigh limit. However, with the presence of measurement's noise,…
Removing the aberrations introduced by the Point Spread Function (PSF) is a fundamental aspect of astronomical image processing. The presence of noise in observed images makes deconvolution a nontrivial task that necessitates the use of…
Obtaining a faithful source intensity distribution map of the sky from noisy data demands incorporating known information of the expected signal, especially when the signal is weak compared to the noise. We introduce a widely used procedure…
Dusty star-forming galaxies (DSFGs) dominate the far-infrared and sub-millimetre number counts, but single-dish surveys suffer from poor angular resolution, complicating mult-wavelength counterpart identification. Prior-driven deblending…
We consider the problem of stable recovery of sparse signals of the form $$F(x)=\sum_{j=1}^d a_j\delta(x-x_j),\quad x_j\in\mathbb{R},\;a_j\in\mathbb{C}, $$ from their spectral measurements, known in a bandwidth $\Omega$ with absolute error…
The aim of this paper is to investigate superresolution in deconvolution driven by sparsity priors. The observed signal is a convolution of an original signal with a continuous kernel.With the prior knowledge that the original signal can be…
We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transforms. Our key…