Sparse Inpainting and Isotropy

Abstract

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 inpainting techniques using the spherical harmonic basis as a dictionary and the isotropy properties of cosmological maps, as for instance those arising from cosmic microwave background (CMB) experiments. In particular, we investigate the possibility that inpainted maps may exhibit anisotropies in the behaviour of higher-order angular polyspectra. We provide analytic computations and simulations of inpainted maps for a Gaussian isotropic model of CMB data, suggesting that the resulting angular trispectrum may exhibit small but non-negligible deviations from isotropy.

18 pages, 6 figures. v3: matches version published in JCAP; formatting changes and single typo correction only. Code available from http://zuserver2.star.ucl.ac.uk/~smf/code.html

References in corpus (7)

• Planck 2013 results. I. Overview of products and scientific results
• Fast optimal CMB power spectrum estimation with Hamiltonian sampling
• Efficient Wiener filtering without preconditioning
• Sparse image reconstruction on the sphere: implications of a new sampling theorem
• Sparsity and the Bayesian Perspective
• Fourier coefficients of invariant random fields on homogeneous spaces of compact groups
• Fast Wiener filtering of CMB maps

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• Sparse image reconstruction on the sphere: a general approach with uncertainty quantification
• Sparse Isotropic Regularization for Spherical Harmonic Representations of Random Fields on the Sphere