相关论文: Smooth maps from clumpy data: generalizations
Smoothing is omnipresent in astronomy, because almost always measurements performed at discrete positions in the sky need to be interpolated into a smooth map for subsequent analysis. Still, the statistical properties of different…
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…
We address the question of astronomical image processing from data obtained with array detectors. We define and analyze the cases of evenly, regularly, and irregularly sampled maps for idealized (i.e., infinite) and realistic (i.e., finite)…
This paper is concerned with applications of the theory of approximation and interpolation based on compensated convex transforms developed in [K. Zhang, E. Crooks, A. Orlando, Compensated convexity methods for approximations and…
We study an estimator for smoothing irregularly sampled data into a smooth map. The estimator has been widely used in astronomy, owing to its low level of noise; it involves a weight function -- or smoothing kernel -- w(\theta). We show…
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…
Galactic all-sky maps at very disparate frequencies, like in the radio and $\gamma$-ray regime, show similar morphological structures. This mutual information reflects the imprint of the various physical components of the interstellar…
By utilizing the idea of Colombeau's generalized function, we introduce a notion of asymptotic map between arbitrary diffeological spaces. The category consisting of diffeological spaces and asymptotic maps is enriched over the category of…
Standard interpolation techniques are implicitly based on the assumption that the signal lies on a homogeneous domain. In this letter, the proposed interpolation method instead exploits prior information about domain inhomogeneity,…
As a higher dimensional version of the theory of Morse functions, there have been various studies of smooth manifolds using generic smooth maps. As fundamental results, in these studies, they have found that inverse images of such maps…
The total generalized variation extends the total variation by incorporating higher-order smoothness. Thus, it can also suffer from similar discretization issues related to isotropy. Inspired by the success of novel discretization schemes…
Sparse inpainting techniques are gaining in popularity as a tool for cosmological data analysis, in particular for handling data which present masked regions and missing observations. We investigate here the relationship between sparse…
A new method for improving the resolution of astronomical images is presented. It is based on the principle that sampled data cannot be fully deconvolved without violating the sampling theorem. Thus, the sampled image should not be…
We present a simple method based on the stability and duality of the properties of sampling and interpolation, which allows one to substantially simplify the proofs of some classical results.
We investigate stochastic interpolation, a recently introduced framework for high dimensional sampling which bears many similarities to diffusion modeling. Stochastic interpolation generates a data sample by first randomly initializing a…
We present a novel method to significantly speed up cosmological parameter sampling. The method relies on constructing an interpolation of the CMB-log-likelihood based on sparse grids, which is used as a shortcut for the…
Successive differences on a sequence of data help to discover some smoothness features of this data. This was one of the main reasons for rewriting the classical interpolation formula in terms of such data differences. The aim of this paper…
Randomly sampling points on surfaces is an essential operation in geometry processing. This sampling is computationally straightforward on explicit meshes, but it is much more difficult on other shape representations, such as widely-used…
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…