Work

Removing the Mask—Reconstructing a Real-Valued Field on the Sphere from a Masked Field by Spherical Fourier Analysis

Year: 2024

Type: article

Abstract: . The paper analyzes 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 specialized 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 realization of a Gaussian random field with an artificial angular power spectrum of moderate degree ([Formula: see text]). The recovery is highly satisfactory in the absence of noise and even in the presence of moderate noise.

Source: SIAM Journal on Imaging Sciences

DOI: 10.1137/23m1603157

Authors: Jan Hamann, Quoc T. Le Gia, Ian H. Sloan, Robert S. Womersley

Institution: UNSW Sydney

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: University of New South Wales, Australian Research Council

Award: Uncertainty on spheres and shells: mathematics and methods for applications