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 ℓ1ℓ1 minimization over a Fourier dictionary, such as the orthonormal system of spherical harmonics.

Cammarota, V., Marinucci, D. (2015). The stochastic properties of l(1)-regularized spherical Gaussian fields. APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 38(2), 262-283 [10.1016/j.acha.2014.04.003].

The stochastic properties of l(1)-regularized spherical Gaussian fields

MARINUCCI, DOMENICO
2015

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 ℓ1ℓ1 minimization over a Fourier dictionary, such as the orthonormal system of spherical harmonics.
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/06 - Probabilita' e Statistica Matematica
English
random fields; spherical harmonics; Gaussianity; isotropy; convex regularization
Cammarota, V., Marinucci, D. (2015). The stochastic properties of l(1)-regularized spherical Gaussian fields. APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS, 38(2), 262-283 [10.1016/j.acha.2014.04.003].
Cammarota, V; Marinucci, D
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/131225
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