Related papers: Stable Super-Resolution of Images: A Theoretical S…
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…
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…
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…
We consider simultaneously identifying the membership and locations of point sources that are convolved with different low-pass point spread functions, from the observation of their superpositions. This problem arises in three-dimensional…
This paper studies the recovery of a superposition of point sources from noisy bandlimited data. In the fewest possible words, we only have information about the spectrum of an object in a low-frequency band bounded by a certain cut-off…
The ability to resolve detail in the object that is being imaged, named by resolution, is the core parameter of an imaging system. Super-resolution is a class of techniques that can enhance the resolution of an imaging system and even…
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…
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 study the problem of super-resolving a superposition of point sources from noisy low-pass data with a cut-off frequency f. Solving a tractable convex program is shown to locate the elements of the support with high precision as long as…
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…
In single-molecule microscopy it is necessary to locate with high precision point sources from noisy observations of the spectrum of the signal at frequencies capped by $f_c$, which is just about the frequency of natural light. This paper…
In super-resolution it is necessary to locate with high precision point sources from noisy observations of the spectrum of the signal at low frequencies capped by f_c. In the case when the point sources are positive and are located on a…
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,…
Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect…
Several applications require the super-resolution of noisy images and the preservation of geometrical and texture features. State-of-the-art super-resolution methods do not account for noise and generally enhance the output image's…
The convolution of a discrete measure, $x=\sum_{i=1}^ka_i\delta_{t_i}$, with a local window function, $\phi(s-t)$, is a common model for a measurement device whose resolution is substantially lower than that of the objects being observed.…
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…
Solving an optimization problem whose objective function is the sum of two convex functions has received considerable interests in the context of image processing recently. In particular, we are interested in the scenario when a…
We consider the problem of recovering a signal consisting of a superposition of point sources from low-resolution data with a cut-off frequency f. If the distance between the sources is under 1/f, this problem is not well posed in the sense…
The stability of spike deconvolution, which aims at recovering point sources from their convolution with a point spread function (PSF), is known to be related to the separation between those sources. When the observations are noisy, it is…