相关论文: A Theory of Computational Resolution Limit for Lin…

We introduce a notion of nuclear numerical range defined as the set of expectation values of a given operator $A$ among normalized pure states, which belong to the nucleus of an auxiliary operator $Z$. This notion proves to be applicable to…

Accurate phase estimation plays a pivotal role in quantum metrology, yet its precision is significantly affected by noise, particularly phase-diffusive noise caused by phase drift. To address this challenge, the joint estimation of phase…

We propose a learning-based approach for estimating the spectrum of a multisinusoidal signal from a finite number of samples. A neural-network is trained to approximate the spectra of such signals on simulated data. The proposed methodology…

The problem of super-resolution in general terms is to recuperate a finitely supported measure $\mu$ given finitely many of its coefficients $\hat{\mu}(k)$ with respect to some orthonormal system. The interesting case concerns situations,…

In the study of condensed matter physics, spectral information plays an important role for understand the mechanism of materials. However, it is difficult to obtain the spectrum directly through experiments or simulation. For example, the…

A joint communication and channel state estimation problem is investigated, in which reliable information transmission over a noisy channel, and high-fidelity estimation of the channel state, are simultaneously sought. The tradeoff between…

This paper considers a sequential estimation and sensor scheduling problem with one sensor and one estimator. The sensor makes sequential observations about the state of an underlying memoryless stochastic process, and makes a decision as…

Spectral density estimation is a core problem of system identification, which is an important research area of system control and signal processing. There have been numerous results on the design of spectral density estimators. However to…

In a mixed generalized linear model, the goal is to learn multiple signals from unlabeled observations: each sample comes from exactly one signal, but it is not known which one. We consider the prototypical problem of estimating two…

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…

Motivated by value function estimation in reinforcement learning, we study statistical linear inverse problems, i.e., problems where the coefficients of a linear system to be solved are observed in noise. We consider penalized estimators,…

This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach,…

This article pursues a statistical study of the Hough transform, the celebrated computer vision algorithm used to detect the presence of lines in a noisy image. We first study asymptotic properties of the Hough transform estimator, whose…

Computational color constancy refers to the problem of computing the illuminant color so that the images of a scene under varying illumination can be normalized to an image under the canonical illumination. In this paper, we adopt a deep…

This paper studies a nonlinear filtering problem over an infinite time interval. The signal to be estimated is driven by a stochastic partial differential equation involves unknown parameters. Based on discrete observation, strongly…

This paper considers the problem of simultaneous sensor fault detection, isolation, and networked estimation of linear full-rank dynamical systems. The proposed networked estimation is a variant of single time-scale protocol and is based on…

This paper focuses on the fundamental aspects of super-resolution, particularly addressing the stability of super-resolution and the estimation of two-point resolution. Our first major contribution is the introduction of two…

Spectroscopy has an illustrious history delivering serendipitous discoveries and providing a stringent testbed for new physical predictions, including applications from trace materials detection, to understanding the atmospheres of stars…

The problem of optimal estimation of linear functionals constructed from the unobserved values of a stochastic sequence with periodically stationary increments based on observations of the sequence with stationary noise is considered. For…

The problem of optimal linear estimation of a linear functional depending on the unknown values of periodically correlated stochastic process from observations of the process with additive noise is considered. Formulas for calculating the…