Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6416916 | Applied and Computational Harmonic Analysis | 2015 | 22 Pages |
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 neither Gaussianity nor isotropy are conserved in general under convex regularization based on â1 minimization over a Fourier dictionary, such as the orthonormal system of spherical harmonics.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Valentina Cammarota, Domenico Marinucci,