Related papers: Least square estimation of phase, frequency and PD…
We characterize the performance of the widely-used least-squares estimator in astrometry in terms of a comparison with the Cramer-Rao lower variance bound. In this inference context the performance of the least-squares estimator does not…
We propose a statistical framework for the problem of parameter estimation from a noisy optomechanical system. The Cram\'er-Rao lower bound on the estimation errors in the long-time limit is derived and compared with the errors of…
In this paper, we propose a probabilistic reduced-dimensional vector autoregressive (PredVAR) model to extract low-dimensional dynamics from high-dimensional noisy data. The model utilizes an oblique projection to partition the measurement…
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…
In the noisy intermediate-scale quantum era, emerging classical-quantum hybrid optimization algorithms, such as variational quantum algorithms (VQAs), can leverage the unique characteristics of quantum devices to accelerate computations…
This note studies a method for the efficient estimation of a finite number of unknown parameters from linear equations, which are perturbed by Gaussian noise. In case the unknown parameters have only few nonzero entries, the proposed…
In this work, we study the robust phase retrieval problem where the task is to recover an unknown signal $\theta^* \in \mathbb{R}^d$ in the presence of potentially arbitrarily corrupted magnitude-only linear measurements. We propose an…
We analytically and numerically investigate the performance of weak-value amplification (WVA) and related parameter estimation methods in the presence of temporally correlated noise. WVA is a special instance of a general measurement…
We estimate $n$ phases (angles) from noisy pairwise relative phase measurements. The task is modeled as a nonconvex least-squares optimization problem. It was recently shown that this problem can be solved in polynomial time via convex…
Analyses of array-valued datasets often involve reduced-rank array approximations, typically obtained via least-squares or truncations of array decompositions. However, least-squares approximations tend to be noisy in high-dimensional…
Oscillator fluctuations are described as the phase or frequency noise spectrum, or in terms of a wavelet variance as a function of the measurement time. The spectrum is generally approximated by the `power law,' i.e., a Laurent polynomial…
We present a general framework to study the simultaneous estimation of multiple phases in the presence of noise as a discretized model for phase imaging. This approach can lead to nontrivial bounds of the precision for multiphase…
In the linear minimum mean square error (LMMSE) estimation for orthogonal frequency division multiplexing (OFDM) systems, the problem about the determination of the algorithm's parameters, especially those related with channel frequency…
In current MIMO mobile communication systems, phase noise can significantly impair performance. To allow for compensation of these impairments, accurate phase noise modeling is necessary. Numerical modeling of the phase noise process at a…
We analyze a simple prefiltered variation of the least squares estimator for the problem of estimation with biased, semi-parametric noise, an error model studied more broadly in causal statistics and active learning. We prove an oracle…
Recent work in online speech spectrogram inversion effectively combines Deep Learning with the Gradient Theorem to predict phase derivatives directly from magnitudes. Then, phases are estimated from their derivatives via least squares,…
This paper introduces a new algorithm to improve the accuracy of numerical phase-averaging in oscillatory, multiscale, differential equations. Phase-averaging is a timestepping method which averages a mapped variable to remove highly…
In multiple-input multiple-output communications, channel estimation is paramount to keep base stations and users on track. This paper proposes a novel PCA-based-principal component analysis-channel estimation approach for MIMO orthogonal…
In this paper, we propose a framework based on sum-of-squares programming to design iterative first-order optimization algorithms for smooth and strongly convex problems. Our starting point is to develop a polynomial matrix inequality as a…
We consider the problem of estimating a signal from noisy circularly-translated versions of itself, called multireference alignment (MRA). One natural approach to MRA could be to estimate the shifts of the observations first, and infer the…