Reconstruction of Missing Data using Iterative Harmonic Expansion
  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.
