Related papers: Mathematical Theory of Computational Resolution Li…
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 work considers the problem of super-resolution. The goal is to resolve a Dirac distribution from knowledge of its discrete, low-pass, Fourier measurements. Classically, such problems have been dealt with parameter estimation methods.…
Quantum imaging exploits the spatial correlations between photons to image object features with a higher resolution than a corresponding classical light source could achieve. Using a quantum correlated $N$-photon state, the method of…
Inverse synthetic aperture radar (ISAR) super-resolution imaging technology is widely applied in space target imaging. However, the performance limits of super-resolution imaging algorithms remain a rarely explored issue. This paper…
The manifestation of the wave nature of light through diffraction imposes limits on the resolution of optical imaging. For over a century, the Abbe-Rayleigh criterion has been utilized to assess the spatial resolution limits of optical…
In this paper we derive information theoretic performance bounds to sensing and reconstruction of sparse phenomena from noisy projections. We consider two settings: output noise models where the noise enters after the projection and input…
In classical optics, there is a well-known resolution limit, called Rayleigh's curse, in the separation of two incoherent optical sources in close proximity. Recently, Tsang et al. revealed that this difficulty may be circumvented in the…
The interplay between computational efficiency and statistical accuracy in high-dimensional inference has drawn increasing attention in the literature. In this paper, we study computational and statistical boundaries for submatrix…
Resolution, usually defined by the Rayleigh criterion or the Full Width at Half Maximum of a Point Spread Function, is a basic property of an image. Here, we present a new statistical definition of image resolution based on the…
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…
Imaging is an important means by which information is gathered regarding the physical world. Spatial resolution and signal-to-noise ratio are underpinning concepts. There is a paucity of rigorous definitions for these quantities, which are…
The recovery of a signal from the magnitude of its Fourier transform, also known as phase retrieval, is of fundamental importance in many scientific fields. It is well known that due to the loss of Fourier phase the problem in 1D is…
Essentially, the idea of improving the resolution of a given imaging system is to enhance its information capacity represented usually by the temporal-bandwidth (or, spatial-spectrum) product. This letter introduces the concept of…
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…
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…
A method for detecting and approximating fault lines or surfaces, respectively, or decision curves in two and three dimensions with guaranteed accuracy is presented. Reformulated as a classification problem, our method starts from a set of…
The problem of imaging extended targets (sources or scatterers) is formulated in the framework of compressed sensing with emphasis on subwavelength resolution. The proposed formulation of the problems of inverse source/scattering is…
Phase retrieval algorithms have become an important component in many modern computational imaging systems. For instance, in the context of ptychography and speckle correlation imaging, they enable imaging past the diffraction limit and…
The support recovery problem consists of determining a sparse subset of a set of variables that is relevant in generating a set of observations, and arises in a diverse range of settings such as compressive sensing, and subset selection in…
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…