Related papers: On the Stable Resolution Limit of Total Variation …
Passive source localization is a well known inverse problem in which we convert the observed measurements into information about the direction of arrivals. In this paper we focus on the optimal resolution of such problem. More precisely, we…
We consider density estimation under measurement error with the Smoothness-Penalized Deconvolution (SPeD) estimator. The estimator has a tuning parameter regulating the smoothness of the estimate, and proper choice of this parameter is…
This work is concerned with the recovery of piecewise constant images from noisy linear measurements. We study the noise robustness of a variational reconstruction method, which is based on total (gradient) variation regularization. We show…
The development of superresolution techniques, i.e., allowing for efficient resolution below the Rayleigh limit, became one of the important branches in contemporary optics and metrology. Recent findings show that perfect spatial mode…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
Restoration of digital images from their degraded measurements has always been a problem of great theoretical and practical importance in numerous applications of imaging sciences. A specific solution to the problem of image restoration is…
We present STARRED, a Point Spread Function (PSF) reconstruction, two-channel deconvolution, and light curve extraction method designed for high-precision photometric measurements in imaging time series. An improved resolution of the data…
Super-resolution techniques overcome the diffraction-limit and get very high resolutions. A category of these techniques, e.g., STED achieves this by creating an illumination spot smaller than the Airy Disk. As a result, points are…
Synthetic aperture sonar (SAS) image resolution is constrained by waveform bandwidth and array geometry. Specifically, the waveform bandwidth determines a point spread function (PSF) that blurs the locations of point scatterers in the…
In this work, super-resolution by 4 compressive sensing methods (OMP, BP, BLOOMP, BP-BLOT) with highly coherent partial Fourier measurements is comparatively studied. An alternative metric more suitable for gauging the quality of spike…
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…
Super-resolution microscopes (such as STED) illuminate samples with a tiny spot, and achieve very high resolution. But structures smaller than the spot cannot be resolved in this way. Therefore, we propose a technique to solve this problem.…
Spectral deconvolution is essential for extracting peak structures that encode material properties and chemical structures, but conventional automated methods often fail when spectra contain high-intensity noise or unknown background…
Rayleigh's criterion for resolving two incoherent point sources has been the most influential measure of optical imaging resolution for over a century. In the context of statistical image processing, violation of the criterion is especially…
Superresolution is one of the key issues at the crossroads of contemporary quantum optics and metrology. Recently, it was shown that for an idealized case of two balanced sources, spatial mode demultiplexing (SPADE) achieves resolution…
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…
Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…
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…
The point-spread function (PSF) is a fundamental property of any astronomical instrument. In interferometers, differing array configurations combined with their $uv$ coverage, and various weighting schemes can produce an irregular but…
The problem of recovering the parameters of a mixture of spike signals convolved with different PSFs is considered. Herein, the spike support is assumed to be known, while the PSFs lie on a manifold. A non-linear least squares estimator of…