相关论文: Mathematical Theory of Computational Resolution Li…
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…
In this paper, we address the problem of recovering point sources from two dimensional low-pass measurements, which is known as super-resolution problem. This is the fundamental concern of many applications such as electronic imaging,…
Already since the work by Abbe and Rayleigh the difficulty of super resolution where one wants to recover a collection of point sources from low-resolved microscopy measurements is thought to be dependent on whether the distance between the…
We establish a simple method to assess the quantum Fisher information required for resolving two incoherent point sources with an imaging system. The resulting Cram\'er-Rao bound shows that the standard Rayleigh limit can be surpassed by…
We provide a quantitative analysis of super-resolution imaging techniques which exploit temporal fluctuations of luminosity of the sources in order to beat the Rayleigh limit. We define an operationally justified resolution gain figure of…
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…
Rayleigh's criterion states that it becomes essentially difficult to resolve two incoherent optical point sources separated by a distance below the width of point spread functions (PSF), namely in the subdiffraction limit. Recently,…
We consider the problem of reconstructing one-dimensional point sources from their Fourier measurements in a bounded interval $[-\Omega, \Omega]$. This problem is known to be challenging in the regime where the spacing of the sources is…
We study the ubiquitous super-resolution problem, in which one aims at localizing positive point sources in an image, blurred by the point spread function of the imaging device. To recover the point sources, we propose to solve a convex…
We establish the multiparameter quantum Cram\'er-Rao bound for simultaneously estimating the centroid, the separation, and the relative intensities of two incoherent optical point sources using alinear imaging system. For equally bright…
We study the support recovery problem for a high-dimensional signal observed with additive noise. With suitable parametrization of the signal sparsity and magnitude of its non-zero components, we characterize a phase-transition phenomenon…
For conventional imaging, the imaging resolution limit is given by the Rayleigh criterion. Exploiting the prior knowledge of imaging object's sparsity and fixed optical system, imaging beyond the conventional Rayleigh limit, which is backed…
Recent work considered the ultimate (quantum) limit of the precision of estimating the distance between two point objects. It was shown that the performance gap between the quantum limit and that of ideal continuum image-plane direct…
No imaging apparatus can produce perfect images: spatial resolution is limited by the Rayleigh diffraction bound that is a consequence of the imager's finite spatial extent. We show some N-photon strategies that permit resolution of details…
We consider the problem of robustly recovering a $k$-sparse coefficient vector from the Fourier series that it generates, restricted to the interval $[- \Omega, \Omega]$. The difficulty of this problem is linked to the superresolution…
This paper studies stable recovery of a collection of point sources from its noisy $M+1$ low-frequency Fourier coefficients. We focus on the super-resolution regime where the minimum separation of the point sources is below $1/M$. We…
We consider simultaneously identifying the membership and locations of point sources that are convolved with different band-limited point spread functions, from the observation of their superpositions. This problem arises in…
Particle tracking in biological imaging is concerned with reconstructing the trajectories, locations, or velocities of the targeting particles. The standard approach of particle tracking consists of two steps: first reconstructing…
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 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…