相关论文: Towards a Mathematical Theory of Super-Resolution

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…

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…

Given an image generated by the convolution of point sources with a band-limited function, the deconvolution problem is to reconstruct the source number, positions, and amplitudes. This problem arises from many important applications in…

We explore a fundamental problem of super-resolving a signal of interest from a few measurements of its low-pass magnitudes. We propose a 2-stage tractable algorithm that, in the absence of noise, admits perfect super-resolution of an…

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 this paper, we analyze the capacity of super-resolution of one-dimensional positive sources. In particular, we consider the same setting as in [arXiv:1904.09186v2 [math.NA]] and generalize the results there to the case of super-resolving…

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 Fourier coefficients. Super-resolution refers to a stable…

We consider imaging of two partially coherent sources and derive the ultimate quantum limits for estimating the separation, location, relative intensity, and coherence factor. We show that super-resolution in the separation is achievable…

We address the problem of super-resolution of point sources from binary measurements, where random projections of the blurred measurement of the actual signal are encoded using only the sign information. The threshold used for binary…

While spike trains are obviously not band-limited, the theory of super-resolution tells us that perfect recovery of unknown spike locations and weights from low-pass Fourier transform measurements is possible provided that the minimum…

In this work we present a new algorithm for data deconvolution that allows the retrieval of the target function with super-resolution with a simple approach that after a precis e measurement of the instrument response function (IRF), the…

Resolving a linear combination of point sources from their band-limited Fourier data is a fundamental problem in imaging and signal processing. With the incomplete Fourier data and the inevitable noise in the measurement, there is a…

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…

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…

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…

In this work, we propose a novel procedure for video super-resolution, that is the recovery of a sequence of high-resolution images from its low-resolution counterpart. Our approach is based on a "sequential" model (i.e., each…

Super-resolution reconstruction techniques entail the utilization of software algorithms to transform one or more sets of low-resolution images captured from the same scene into high-resolution images. In recent years, considerable…

Frequency estimation from measurements corrupted by noise is a fundamental challenge across numerous engineering and scientific fields. Among the pivotal factors shaping the resolution capacity of any frequency estimation technique are…

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…

Sub-diffraction-limit resolution, or super-resolution, had been successfully demonstrated by recent theoretical and experimental studies for two-point sources with ideal equal-brightness and strict incoherenceness. Unfortunately, practical…