Reconstruction of Missing Data using Iterative Harmonic Expansion
arXiv:1305.0116 · doi:10.1093/mnras/stw1664
Abstract
In the cosmic microwave background or galaxy density maps, missing fluctuations in masked regions can be reconstructed from fluctuations in the surrounding unmasked regions if the original fluctuations are sufficiently smooth. One reconstruction method involves applying a harmonic expansion iteratively to fluctuations in the unmasked region. In this paper, we discuss how well this reconstruction method can recover the original fluctuations depending on the prior of fluctuations and property of the masked region. The reconstruction method is formulated with an asymptotic expansion in terms of the size of mask for a fixed iteration number. The reconstruction accuracy depends on the mask size, the spectrum of the underlying density fluctuations, the scales of the fluctuations to be reconstructed and the number of iterations. For Gaussian fluctuations with the Harrison--Zel'dovich spectrum, the reconstruction method provides more accurate restoration than naive methods based on brute--forth matrix inversion or the singular value decomposition. We also demonstrate that an isotropic non-Gaussian prior does not change the results but an anisotropic non-Gaussian prior can yield a higher reconstruction accuracy compared to the Gaussian prior case.
13 pages, 14 figures, published in MNRAS
References in corpus (19)
- Hemispherical power asymmetry in the three-year Wilkinson Microwave Anisotropy Probe sky maps
- The Uncorrelated Universe: Statistical Anisotropy and the Vanishing Angular Correlation Function in WMAP Years 1-3
- Inflationary perturbations in anisotropic backgrounds and their imprint on the CMB
- Local Voids as the Origin of Large-angle Cosmic Microwave Background Anomalies I
- Anisotropic Cosmological Constant and the CMB Quadrupole Anomaly
- Asymmetric Beams and CMB Statistical Anisotropy
- Local Voids as the Origin of Large-angle Cosmic Microwave Background Anomalies: The Effect of a Cosmological Constant
- The CMB cold spot: texture, cluster or void?
- Cross-correlation of 2MASS and WMAP3: Implications for the Integrated Sachs-Wolfe effect
- On the CMB large-scales angular correlations
- A low CMB variance in the WMAP data
- CMB data analysis and sparsity
- Anomalies in the low CMB multipoles and extended foregrounds
- Planck CMB Anomalies: Astrophysical and Cosmological Secondary Effects and the Curse of Masking
- Can a primordial magnetic field originate large-scale anomalies in WMAP data?
- CMB Alignment in Multi-Connected Universes
- Can residuals of the Solar system foreground explain low multipole anomalies of the CMB ?
- Cosmic Microwave Background Anisotropy from Nonlinear Structures in Accelerating Universes
- Harmonic Inpainting of the Cosmic Microwave Background Sky: Formulation and Error Estimate