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The dictionary approach for spherical deconvolution

Rivoirard, Vincent; Pham Ngoc, Thanh Mai (2013), The dictionary approach for spherical deconvolution, Journal of Multivariate Analysis, 115, p. 138-156. http://dx.doi.org/10.1016/j.jmva.2012.08.011

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00616519/fr/
Date
2013
Journal name
Journal of Multivariate Analysis
Volume
115
Publisher
Elsevier
Pages
138-156
Publication identifier
http://dx.doi.org/10.1016/j.jmva.2012.08.011
Metadata
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Author(s)
Rivoirard, Vincent
Pham Ngoc, Thanh Mai
Abstract (EN)
We consider the problem of estimating a density of probability from indirect data in the spherical convolution model. We aim at building an estimate of the unknown density as a linear combination of functions of an overcomplete dictionary. The procedure is devised through a well-calibrated l1-penalized criterion. The spherical deconvolution setting has been barely studied so far, and the two main approches to this problem, namely the SVD and the hard thresholding ones considered only one basis at a time. The dictionary approach allows to combine various bases and thus enhances estimates sparsity. We provide an oracle inequality under global coherence assumptions. Moreover, the calibrated procedure that we put forward gives very satisfying results in the numerical study when compared with other procedures.
Subjects / Keywords
Second generation wavelets; Sparsity; Calibration; Oracle inequalities; Lasso estimate; Dictionary; Density deconvolution

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