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arXiv · 1309.3459

The Stochastic Properties of $\ell^1$-Regularized Spherical Gaussian Fields

Valentina Cammarota·Domenico Marinucci
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Abstract

Convex regularization techniques are now widespread tools for solving inverse problems in a variety of different frameworks. In some cases, the functions to be reconstructed are naturally viewed as realizations from random processes; an important question is thus whether such regularization techniques preserve the properties of the underlying probability measures. We focus here on a case which has produced a very lively debate in the cosmological literature, namely Gaussian and isotropic spherical random fields, and we prove that Gaussianity and isotropy are not conserved in general under convex regularization over a Fourier dictionary, such as the orthonormal system of spherical harmonics.

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Valentina Cammarota, Domenico Marinucci. 2013-09-13. The Stochastic Properties of $\ell^1$-Regularized Spherical Gaussian Fields. https://doi.org/10.1016/j.acha.2014.04.003

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