Removing the mask -- reconstructing a scalar field on the sphere from a masked field

Abstract

The paper analyses a spectral approach to reconstructing a scalar field on the sphere, given only information about a masked version of the field together with precise information about the (smooth) mask. The theory is developed for a general mask, and later specialised to the case of an axially symmetric mask. Numerical experiments are given for the case of an axial mask motivated by the cosmic microwave background, assuming that the underlying field is a realisation of a Gaussian random field with an artificial angular power spectrum of moderate degree ($\ell \le 100$). The recovery is highly satisfactory in the absence of noise and even in the presence of moderate noise.

References in corpus (13)

• HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
• A unified pseudo-$C_{\ell }$ framework
• Low-order multipole maps of CMB anisotropy derived from WMAP
• CMB data analysis and sparsity
• Filling in CMB map missing data using constrained Gaussian realizations
• Low-l CMB Analysis and Inpainting
• Using inpainting to construct accurate cut-sky CMB estimators
• Recovering the CMB Signal with Machine Learning
• Harmonic in-painting of CMB sky by constrained Gaussian realization
• Inpainting Galactic Foreground Intensity and Polarization maps using Convolutional Neural Network
• Harmonic Inpainting of the Cosmic Microwave Background Sky: Formulation and Error Estimate
• Inpainting CMB maps using Partial Convolutional Neural Networks
• Reconstruction of Missing Data using Iterative Harmonic Expansion