Related papers: Interpolation and smoothing
In a series of papers (Lombardi & Schneider 2001, 2002) we studied in detail the statistical properties of an interpolation technique widely used in astronomy. In particular, we considered the average interpolated map and its covariance…
Interpolation techniques play a central role in Astronomy, where one often needs to smooth irregularly sampled data into a smooth map. In a previous article (Lombardi & Schneider 2001), we have considered a widely used smoothing technique…
We present a new technique for the interpolation of discretely-sampled non-negat ive scalar fields across regions of missing data. Any set of basis functions can be used, though the method is fastest when they are close to orthogonal. We…
Using a deterministic framework allows us to estimate a function with the purpose of interpolating data in spatial statistics. Radial basis functions are commonly used for scattered data interpolation in a d-dimensional space, however,…
The error between appropriately smooth functions and their radial basis function interpolants, as the interpolation points fill out a bounded domain in R^d, is a well studied artifact. In all of these cases, the analysis takes place in a…
In areas such as kernel smoothing and non-parametric regression there is emphasis on smooth interpolation and smooth statistical models. Splines are known to have optimal smoothness properties in one and higher dimensions. It is shown, with…
We present a new method of interpolation for the pixel brightness estimation in astronomical images. Our new method is simple and easily implementable. We show the comparison of this method with the widely used linear interpolation and…
In the era of big data, we first need to manage the data, which requires us to find missing data or predict the trend, so we need operations including interpolation and data fitting. Interpolation is a process to discover deducing new data…
Constructing a propagation map from a set of scattered measurements finds important applications in many areas, such as localization, spectrum monitoring and management. Classical interpolation-type methods have poor performance in regions…
This paper highlights methods from geostatistics that are relevant to the interpretation, intercomparison, and synthesis of atmospheric model data, with a specific application to exoplanet atmospheric modeling. Climate models are…
We find sufficient conditions for a discrete sequence to be interpolating or sampling for certain generalized Bergman spaces on open Riemann surfaces. As in previous work of Bendtsson, Ortega-Cerda, Seip, Wallsten and others, our conditions…
A fundamental building block for supporting better utilization of radio spectrum involves predicting the impact that an emitter will have at different geographic locations. To this end, fixed sensors can be deployed to spatially sample the…
Climate modelers generally require meteorological information on regular grids, but monitoring stations are, in practice, sited irregularly. Thus, there is a need to produce public data records that interpolate available data to a high…
The combination of several socio-economic data bases originating from different administrative sources collected on several different partitions of a geographic zone of interest into administrative units induces the so called areal…
Interferometry is a powerful technique for making sensitive, high-fidelity images of the sky, but is limited in its ability to measure extended or diffuse emission. Better images of extended astronomical objects can be obtained by…
In Helio- and asteroseismology, it is important to have continuous, uninterrupted, data sets. However, seismic observations usually contain gaps and we need to take them into account. In particular, if the gaps are not randomly distributed,…
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…
The next generation of galaxy surveys, aiming to observe millions of galaxies, are expensive both in time and cost. This raises questions regarding the optimal investment of this time and money for future surveys. In a previous work, it was…
We study interpolation inequalities between H\"older Integral Probability Metrics (IPMs) in the case where the measures have densities on closed submanifolds. Precisely, it is shown that if two probability measures $\mu$ and $\mu^\star$…
This work investigates the stability of (discrete) empirical interpolation for nonlinear model reduction and state field approximation from measurements. Empirical interpolation derives approximations from a few samples (measurements) via…