相关论文: Smooth maps from clumpy data: Covariance analysis

Cosmological weak lensing is the powerful probe of cosmology. Here we address one of the most fundamental, statistical questions inherent in weak lensing cosmology: whether or not we can recover the initial Gaussian information content of…

Multiple rotation averaging is an essential task for structure from motion, mapping, and robot navigation. The task is to estimate the absolute orientations of several cameras given some of their noisy relative orientation measurements. The…

A large amount of quantitative geospatial data are collected and aggregated in discrete enumeration units (e.g. countries or states). Smooth pycnophylactic interpolation aims to find a smooth, nonnegative function such that the area…

We compare a recently proposed multivariate spline based on mixed partial derivatives with two other standard splines for the scattered data smoothing problem. The splines are defined as the minimiser of a penalised least squares…

This paper is related to our previous works [1][2] on the error estimate of the averaging technique, for systems with one fast angular variable. In the cited references, a general method (of mixed analytical and numerical type) has been…

We consider imaging of fast moving small objects in space, such as low earth orbit satellites. The imaging system consists of ground based, asynchronous sources of radiation and several passive receivers above the dense atmosphere. We use…

Inspired by the key principle behind the EM algorithm, we propose a general methodology for conducting wavelet estimation with irregularly-spaced data by viewing the data as the observed portion of an augmented regularly-spaced data set. We…

Probabilistic smoothing is a standard tool for global optimization, but existing methods rely on Gaussian kernels and specific transforms, often resulting in strong hyperparameter sensitivity and limited robustness. We propose a general…

In this paper, we revisit the rotation averaging problem applied in global Structure-from-Motion pipelines. We argue that the main problem of current methods is the minimized cost function that is only weakly connected with the input data…

In this work, we address the problem of polynomial interpolation of non-pointwise data. More specifically, we assume that our input information comes from measurements obtained on diffuse compact domains. Although the nodal and the diffused…

A continuing mystery in understanding the empirical success of deep neural networks is their ability to achieve zero training error and generalize well, even when the training data is noisy and there are more parameters than data points. We…

In this article, we consider the problem of approximating a finite set of data (usually huge in applications) by invariant subspaces generated through a small set of smooth functions. The invariance is either by translations under a…

We consider the problem of estimating a spatially varying density function, motivated by problems that arise in large-scale radiological survey and anomaly detection. In this context, the density functions to be estimated are the background…

The singular value matrix decomposition plays a ubiquitous role throughout statistics and related fields. Myriad applications including clustering, classification, and dimensionality reduction involve studying and exploiting the geometric…

We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other…

The paper has two main goals. The first is to take a new approach to rearrangements on certain classes of measurable real-valued functions on $\mathbb{R}^n$. Rearrangements are maps that are monotonic (up to sets of measure zero) and…

Three independent techniques are used to separate fine structure from the absorption spectra, the background function in which is approximated by (i) smoothing spline. We propose a new reliable criterion for determination of smoothing…

Observational data, especially astrophysical data, is often limited by gaps in data that arises due to lack of observations for a variety of reasons. Such inadvertent gaps are usually smoothed over using interpolation techniques. However…

Quantitative morphologies, such as asymmetry and concentration, have long been used as an effective way to assess the distribution of galaxy starlight in large samples. Application of such quantitative indicators to other data products…

In this paper, we consider the problem of estimating the covariance kernel and its eigenvalues and eigenfunctions from sparse, irregularly observed, noise corrupted and (possibly) correlated functional data. We present a method based on…