Related papers: Cramer-Rao bound in detection of reversals
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a…
Standard conformal anomaly detection provides marginal finite-sample guarantees under the assumption of exchangeability . However, real-world data often exhibit distribution shifts, necessitating a weighted conformal approach to adapt to…
Complex geometries can be easily treated using the well-known full-way and half-way bounce-back rules. However, the accuracy of the full-way bounce-back rule is one order lower than the half-way bounce-back rule. Moreover, when the walls…
The problem of detection of magnetic fields using NV centers, that is, to check whether a weak magnetic field is present or not, can be tackled using quantum state discrimination theory. In this regard, we find the POVMs that maximize the…
The Cram\'er-Rao bound serves as a crucial lower limit for the mean squared error of an estimator in frequentist parameter estimation. Paradoxically, it requires highly accurate prior knowledge of the estimated parameter for constructing…
The concept of time reversal (TR) of scalar wave is reexamined from basic principles. Five different time reversal mirrors (TRM) are introduced and their relations are analyzed. For the boundary behavior, it is shown that for paraxial wave…
In practical nonlinear filtering, the assessment of achievable filtering performance is important. In this paper, we focus on the problem of efficiently approximate the posterior Cramer-Rao lower bound (CRLB) in a recursive manner. By using…
This paper is dedicated to design a direct sampling method of inverse electromagnetic scattering problems, which uses multi-frequency sparse backscattering far field data for reconstructing the boundary of perfectly conducting obstacles. We…
Convergence rates in spectral regularization methods quantify the approximation error in inverse problems as a function of the noise level or the number of sampling points. Classical strong convergence rate results typically rely on source…
To achieve the joint active and passive beamforming gains in the reconfigurable intelligent surface assisted millimeter wave system, the reflected cascade channel needs to be accurately estimated. Many strategies have been proposed in the…
The micromaser is examined with the aim of understanding certain of its properties based on a time-reversed quantum trajectory analysis. The background theory of master equations derived from a repeated interaction model perspective is…
This paper studies distance estimation for diffusive molecular communication. The Cramer-Rao lower bound on the variance of the distance estimation error is derived. The lower bound is derived for a physically unbounded environment with…
In this paper, the Cramer Rao bound (CRB) for range estimation between two underwater nodes is calculated under a Gaussian noise assumption on the measurements. The nodes can measure their depths, their mutual time of flight, and they have…
Every sufficiently big matrix with small spectral norm has a nearby low-rank matrix if the distance is measured in the maximum norm (Udell & Townsend, SIAM J Math Data Sci, 2019). We use the Hanson--Wright inequality to improve the estimate…
We use variational convergence to derive a hierarchy of one-dimensional rod theories, starting out from three-dimensional models in nonlinear elasticity subject to local volume-preservation. The densities of the resulting $\Gamma$-limits…
Low-rank matrix factorizations arise in a wide variety of applications -- including recommendation systems, topic models, and source separation, to name just a few. In these and many other applications, it has been widely noted that by…
Computational time reversal imaging can be used to locate the position of multiple scatterers in a known background medium. The current methods for computational time reversal imaging are based on the null subspace projection operator,…
We consider for the time-dependent Maxwell's equations the inverse problem of identifying locations and certain properties of small electromagnetic inhomogeneities in a homogeneous background medium from dynamic measurements of the…
A fundamental question in Dynamical Systems is to identify regions of phase/parameter space satisfying a given property (stability, linearization, etc). Given a family of analytic circle diffeomorphisms depending on a parameter, we obtain…
The wave equation is time-reversal invariant. The enclosure method using a Neumann data generated by this invariance is introduced. The method yields the minimum ball that is centered at a given arbitrary point and encloses an unknown…