Related papers: Least square estimation of phase, frequency and PD…

Shrinkage estimation usually reduces variance at the cost of bias. But when we care only about some parameters of a model, I show that we can reduce variance without incurring bias if we have additional information about the distribution of…

High data rates require vast bandwidths, that can be found in the sub-THz band, and high sampling frequencies, which are predicted to lead to a problematically high analog-to-digital converter (ADC) power consumption. It was proposed to use…

We derive the ultimate bounds on the performance of nonlinear measurement schemes in the presence of noise. In particular, we investigate the precision of the second-order estimation scheme in the presence of the two most detrimental types…

Variational Physics-Informed Neural Networks often suffer from poor convergence when using stochastic gradient-descent-based optimizers. By introducing a Least Squares solver for the weights of the last layer of the neural network, we…

Derivative Free Optimization is known to be an efficient and robust method to tackle the black-box optimization problem. When it comes to noisy functions, classical comparison-based algorithms are slower than gradient-based algorithms. For…

We propose and analyse numerical algorithms based on weighted least squares for the approximation of a real-valued function on a general bounded domain $\Omega \subset \mathbb{R}^d$. Given any $n$-dimensional approximation space $V_n…

Monte Carlo studies of many quantum systems face exponentially severe signal-to-noise problems. We show that noise arising from complex phase fluctuations of observables can be reduced without introducing bias using path integral contour…

We present a priori and a posteriori error analysis of a Virtual Element Method (VEM) to approximate the vibration frequencies and modes of an elastic solid. We analyze a variational formulation relying only on the solid displacement and…

In this letter we study the design of algorithms for estimation of phase noise (PN) with colored noise sources. A soft-input maximum a posteriori PN estimator and a modified soft-input extended Kalman smoother are proposed. The performance…

Standard quantum amplitude estimation algorithms provide quadratic speedup to Monte-Carlo simulations but require a circuit depth that scales as inverse of the estimation error. In view of the shallow depth in near-term devices, the…

The fundamental multidimensional line spectral estimation problem is addressed utilizing the Bayesian methods. Motivated by the recently proposed variational line spectral estimation (VALSE) algorithm, multidimensional VALSE (MDVALSE) is…

This paper provides an alternative to penalized estimators for estimation and vari- able selection in high dimensional linear regression models with measurement error or missing covariates. We propose estimation via bias corrected least…

Improving multiparameter quantum estimation in magnonic systems via quantum noise suppression is a well-established and critical research objective. In this work, we propose an experimentally realistic scheme to improve the precision of…

The performance of speech and events recognition systems significantly improved recently thanks to deep learning methods. However, some of these tasks remain challenging when algorithms are deployed on robots due to the unseen mechanical…

Achieving quantum-enhanced performances when measuring unknown quantities requires developing suitable methodologies for practical scenarios, that include noise and the availability of a limited amount of resources. Here, we report on the…

When recovering an unknown signal from noisy measurements, the computational difficulty of performing optimal Bayesian MMSE (minimum mean squared error) inference often necessitates the use of maximum a posteriori (MAP) inference, a special…

A new method for designing non-uniform filter-banks for acoustic echo cancellation is proposed. In the method, the analysis prototype filter design is framed as a convex optimization problem that maximizes the signal-to-alias ratio (SAR) in…

This paper presents a reduced-order approach for four-dimensional variational data assimilation, based on a prior EO F analysis of a model trajectory. This method implies two main advantages: a natural model-based definition of a mul…

We address the use of optical parametric oscillator (OPO) to counteract phase-noise in quantum optical communication channels, and demonstrate reduction of phase diffusion for coherent signals travelling through a suitably tuned OPO. In…

Alternating minimization, or Fienup methods, have a long history in phase retrieval. We provide new insights related to the empirical and theoretical analysis of these algorithms when used with Fourier measurements and combined with convex…