Related papers: A spectral mean for point sampled closed curves
Given data drawn from a collection of Gaussian variables with a common mean but different and unknown variances, what is the best algorithm for estimating their common mean? We present an intuitive and efficient algorithm for this task. As…
We study the 2D Navier-Stokes equation with transport noise subject to periodic boundary conditions. Our main result is an error estimate for the time-discretisation showing a convergence rate of order (up to) 1/2. It holds with respect to…
This paper investigates the convergence properties of spectral algorithms -- a class of regularization methods originating from inverse problems -- under covariate shift. In this setting, the marginal distributions of inputs differ between…
Scan matching is a widely used technique in state estimation. Point-cloud alignment, one of the most popular methods for scan matching, is a weighted least-squares problem in which the weights are determined from the inverse covariance of…
Let $Y$ be a stochastic process on $[0,1]$ satisfying $dY(t) = n^{1/2} f(t) dt + dW(t)$, where $n \ge 1$ is a given scale parameter (``sample size''), $W$ is standard Brownian motion and $f$ is an unknown function. Utilizing suitable…
This paper considers edge interval estimation between two regions of a Synthetic Aperture Radar (SAR) image which differ in texture. This is a difficult task because SAR images are contaminated with speckle noise. Different point estimation…
A hybrid estimator of the log-spectral density of a stationary time series is proposed. First, a multiple taper estimate is performed, followed by kernel smoothing the log-multitaper estimate. This procedure reduces the expected mean square…
Data-driven machine learning models are being increasingly employed in several important inference problems in biology, chemistry, and physics which require learning over combinatorial spaces. Recent empirical evidence (see, e.g., [1], [2],…
We present an all-sky map of the synchrotron spectral index and curvature between 45 and 2300 MHz at a resolution of 1 degree calculated from a combination of numerous partial sky empirical measurements. We employ a least-squares parametric…
The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…
We study zero-shot conditional sampling with pretrained diffusion models for linear inverse problems, including inpainting and super-resolution. In these problems, the observation determines only part of the unknown signal. The remaining…
A simple, yet general, formalism for the optimized linear combination of astrophysical images is constructed and demonstrated. The formalism allows the user to combine multiple undersampled images to provide oversampled output at high…
It is known that waves generated by ambient noise sources and recorded by passive receivers can be used to image the reflectivities of an unknown medium. However, reconstructing the reflectivity of the medium from partial boundary…
Estimating position and orientation change of a mobile platform from two consecutive point clouds provided by a high-resolution sensor is a key problem in autonomous navigation. In particular, scan matching algorithms aim to find the…
The high energy physics unfolding problem is an important statistical inverse problem in data analysis at the Large Hadron Collider (LHC) at CERN. The goal of unfolding is to make nonparametric inferences about a particle spectrum from…
A general purpose fitting model for one-dimensional astrometric signals is developed, building on a maximum likelihood framework, and its performance is evaluated by simulation over a set of realistic image instances. The fit quality is…
We consider the high energy physics unfolding problem where the goal is to estimate the spectrum of elementary particles given observations distorted by the limited resolution of a particle detector. This important statistical inverse…
In the near future, millions of load curves measuring the electricity consumption of French households in small time grids (probably half hours) will be available. All these collected load curves represent a huge amount of information which…
The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…
Nonparametric estimators for the mean and the covariance functions of functional data are proposed. The setup covers a wide range of practical situations. The random trajectories are, not necessarily differentiable, have unknown regularity,…