The dictionary approach for spherical deconvolution

JOURNAL OF MULTIVARIATE ANALYSIS

卷:115

Article

Thanh Mai Pham Ngoc¹  Rivoirard, Vincent² 

[1] Univ Paris 11, UMR CNRS 8628, Math Lab, F-91405 Orsay, France

[2] Univ Paris 09, CEREMADE UMR CNRS 7534, F-75775 Paris 16, France

关键词: Density deconvolution;    Dictionary;    Lasso estimate;    Oracle inequalities;    Calibration;    Sparsity;    Second generation wavelets;   

DOI  :  10.1016/j.jmva.2012.08.011

来源: Elsevier

【 摘 要 】

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 l(1)-penalized criterion. The spherical deconvolution setting has been barely studied so far, and the two main approaches 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 quite satisfying results in the numerical study when compared with other procedures. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free