Related papers: Super-resolution meets machine learning: approxima…
This paper develops a mathematical theory of super-resolution. Broadly speaking, super-resolution is the problem of recovering the fine details of an object---the high end of its spectrum---from coarse scale information only---from samples…
Super-resolution is the problem of recovering a superposition of point sources using bandlimited measurements, which may be corrupted with noise. This signal processing problem arises in numerous imaging problems, ranging from astronomy to…
We consider the limits of super-resolution using imaging constraints. Due to various theoretical and practical limitations, reconstruction-based methods have been largely restricted to small increases in resolution. In addition, motion-blur…
Super-resolution is generally referred to as the task of recovering fine details from coarse information. Motivated by applications such as single-molecule imaging, radar imaging, etc., we consider parameter estimation of complex…
Super-resolution results are usually measured by full-reference image quality metrics or human rating scores. However, these evaluation methods are general image quality measurement, and do not account for the nature of the super-resolution…
Super-resolution is a fundamental task in imaging, where the goal is to extract fine-grained structure from coarse-grained measurements. Here we are interested in a popular mathematical abstraction of this problem that has been widely…
Let $M(\mathbb{T}^d)$ be the space of complex bounded Radon measures defined on the $d$-dimensional torus group $(\mathbb{R}/\mathbb{Z})^d=\mathbb{T}^d$, equipped with the total variation norm $\|\cdot\|$; and let $\hat\mu$ denote the…
The problem of super-resolution, roughly speaking, is to reconstruct an unknown signal to high accuracy, given (potentially noisy) information about its low-degree Fourier coefficients. Prior results on super-resolution have imposed strong…
In this paper, we address the problem of reconstruction of support of a measure from its moments. More precisely, given a finite subset of the moments of a measure, we develop a semidefinite program for approximating the support of measure…
Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral…
Super-resolution is a machine-learning technique in image processing which generates high-resolution images from low-resolution images. Inspired by this approach, we perform a numerical experiment of quantum machine learning, which takes…
This work aims to reconstruct image sequences with Total Variation regularity in super-resolution. We consider, in particular, images of scenes for which the point-to-point image transformation is a plane projective transformation. We first…
We study the problem of reconstructing a positive discrete measure on a compact set $K \subseteq \mathbb{R}^n$ from a finite set of moments (possibly known only approximately) via convex optimization. We give new uniqueness results, new…
This paper provides a theoretical analysis of diffraction-limited superresolution, demonstrating that arbitrarily close point sources can be resolved in ideal situations. Precisely, we assume that the incoming signal is a linear combination…
Super-resolution is a fundamental problem in computer vision which aims to overcome the spatial limitation of camera sensors. While significant progress has been made in single image super-resolution, most algorithms only perform well on…
Super-resolution is aimed at reconstructing high-resolution images from low-resolution observations. State-of-the-art approaches underpinned with deep learning allow for obtaining outstanding results, generating images of high perceptual…
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 inverse problem is $1/M$ and super-resolution refers to…
Self-supervised learning is crucial for super-resolution because ground-truth images are usually unavailable for real-world settings. Existing methods derive self-supervision from low-resolution images by creating pseudo-pairs or by…
In this paper we establish accuracy bounds of Prony's method (PM) for recovery of sparse measures from incomplete and noisy frequency measurements, or the so-called problem of super-resolution, when the minimal separation between the points…
Superresolution refers to the estimation of parameters of an image with an accuracy beyond standard classical techniques such as direct detection. In seminal work by Lu et al., a measurement to estimate the separation distance of two point…