Related papers: Analysis of the sparse super resolution limit usin…

We analyze the far field resolution of apertures which are illuminated by a point dipole located at subwavelength distances. It is well known that radiation emitted by a localized source can be considered a combination of travelling and…

Recently, it has been proved in Babadi et al. that in noisy compressed sensing, a joint typical estimator can asymptotically achieve the Cramer-Rao lower bound of the problem.To prove this result, this paper used a lemma,which is provided…

This paper presents Cram\'er-Rao Lower Bound (CRLB) for the complex-valued Blind Source Extraction (BSE) problem based on the assumption that the target signal is independent of the other signals. Two instantaneous mixing models are…

Point source localization is a problem of persistent interest in optical imaging. In particular, a number of widely used biological microscopy techniques rely on precise three-dimensional localization of single fluorophores. As emitter…

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…

We study recovery of amplitudes and nodes of a finite impulse train from noisy frequency samples. This problem is known as super-resolution under sparsity constraints and has numerous applications. An especially challenging scenario occurs…

In traditional optical imaging systems, the spatial resolution is limited by the physics of diffraction, which acts as a low-pass filter. The information on sub-wavelength features is carried by evanescent waves, never reaching the camera,…

This paper focusses on the sparse estimation in the situation where both the the sensing matrix and the measurement vector are corrupted by additive Gaussian noises. The performance bound of sparse estimation is analyzed and discussed in…

In this paper we use the Cramer-Rao lower uncertainty bound to estimate the maximum precision that could be achieved on the joint simultaneous (or 2D) estimation of photometry and astrometry of a point source measured by a linear CCD…

Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…

Let A be an n by m matrix with m>n, and suppose that the underdetermined linear system As=x admits a sparse solution s0 for which ||s0||_0 < 1/2 spark(A). Such a sparse solution is unique due to a well-known uniqueness theorem. Suppose now…

We present a new proof of the quantum Cramer-Rao bound for precision parameter estimation [1-3] and extend it to a more general class of measurement procedures. We analyze a generalized framework for parameter estimation that covers most…

Recent theoretical and experimental work has shown that the quantum Fisher information associated with estimating the separation between two optical point sources remains finite at small separations, effectively opening new routes to…

The performance bounds of near-field sensing are studied for circular arrays, focusing on the impact of bandwidth and array size. The closed-form Cramer-Rao bound (CRBs) for angle and distance estimation are derived, revealing the scaling…

We use the Cramer-Rao bound to show which short magnetic reversals can be recovered successfully from a magnetic anomaly profile. Using a simple variant of the Vine-Matthews model, we show, in particular, that errors in determining the…

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…

Super-resolution theory aims to estimate the discrete components lying in a continuous space that constitute a sparse signal with optimal precision. This work investigates the potential of recent super-resolution techniques for spectral…

In this work, we introduce a novel approach for determining a joint sparse spectrum from several non-uniformly sampled data sets, where each data set is assumed to have its own, possibly disjoint, and only partially known, sampling times.…

Quantum number-path entanglement is a resource for super-sensitive quantum metrology and in particular provides for sub-shotnoise or even Heisenberg-limited sensitivity. However, such number-path entanglement has thought to have been…

Previous work established fundamental bounds on subwavelength resolution for the radar range resolution problem, called superradar [Phys. Rev. Appl. 20, 064046 (2023)]. In this work, we identify the optimal waveforms for distinguishing the…