Related papers: Analysis of the sparse super resolution limit usin…
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…
Motivated by the problem of determining the atomic structure of macromolecules using single-particle cryo-electron microscopy (cryo-EM), we study the sample and computational complexities of the sparse multi-reference alignment (MRA) model:…
Precision and accuracy, as two crucial criteria for quantum metrology, have previously lacked rigorous definitions and distinctions. In this paper, we provide a unified definition of precision and accuracy from the perspective of…
The posterior Cram\'er-Rao lower bound (PCRLB) derived in Tichavsk\'y et al., 1998, provides a bound on the mean square error (MSE) obtained with any non-linear state filter. Computing the PCRLB involves solving complex, multi-dimensional…
The last decade has seen numerous efforts to achieve imaging resolution beyond that of the Abbe-Rayleigh diffraction limit. The main direction of research aiming to break this limit seeks to exploit the evanescent components containing fine…
Achieving resolution in the sub-Rayleigh regime (superresolution) is one of the rapidly developing topics in quantum optics and metrology. Recently, it was shown that perfect measurement based on spatial mode demultiplexing (SPADE) 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…
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…
Improvement of label-free far-field resolution of optical imaging is possible with prior knowledge of the object such as its sparsity or accumulated by a posteriori examination of a similar class of object1-4. We show that the sole…
This paper derives a general expression for the Cram\'er-Rao bound (CRB) of wireless localization algorithms using range measurements subject to bias corruption. Specifically, the a priori knowledge about which range measurements are…
This paper presents a Cramer-Rao bound (CRB) for the estimation of parameters confined to an arbitrary set. Unlike existing results that rely on equality or inequality constraints, manifold structures, or the nonsingularity of the Fisher…
We generalize the theory of resolving a mixture of two closely spaced spontaneous emission lifetimes to include pure dephasing contributions to decoherence, leading to the resurgence of Rayleigh's Curse at small lifetime separations.…
Estimating the angular separation between two incoherent thermal sources is a challenging task for direct imaging, especially when it is smaller than or comparable to the Rayleigh length. In addition, the task of discriminating whether…
We determine the ultimate potential of quantum imaging for boosting the resolution of a far-field, diffraction-limited, linear imaging device within the paraxial approximation. First we show that the problem of estimating the separation…
We investigate the recovery of nodes and amplitudes from noisy frequency samples in spike train signals, also known as the super-resolution (SR) problem. When the node separation falls below the Rayleigh limit, the problem becomes…
Aims. We investigate the maximum astrometric precision that can be reached on moving targets observed with digital-sensor arrays, and provide an estimate for its ultimate lower limit based on the Cram\'er-Rao bound. Methods. We extend…
The super-resolution theory developed recently by Cand\`{e}s and Fernandes-Granda aims to recover fine details of a sparse frequency spectrum from coarse scale information only. The theory was then extended to the cases with compressive…
We investigate analytically and numerically the role of quantum fluctuations in reconstruction of optical objects from diffraction-limited images. Taking as example of an input object two closely spaced Gaussian peaks we demonstrate that…
The Rayleigh criterion has long served as a fundamental limit for the resolution of optical imaging. Recent advances in multiparameter quantum metrology have led to quantum superresolution that can break this limit and achieve nonvanishing…
The Rayleigh diffraction bound sets the minimum separation for two point objects to be distinguishable in a conventional imaging system. We demonstrate resolution enhancement beyond the Rayleigh bound using random scanning of a…