Application of second generation wavelets to blind spherical deconvolution

JOURNAL OF MULTIVARIATE ANALYSIS

卷:124

Article

Vareschi, T.^1,2 

[1] Univ Paris 07, F-75013 Paris, France

[2] CNRS UMR 7099, F-75013 Paris, France

关键词: Blind deconvolution;    Blockwise SVD;    Spherical deconvolution;    Second generation wavelets;    Nonparametric adaptive estimation;    Linear inverse problems;   

DOI  :  10.1016/j.jmva.2013.11.012

来源: Elsevier

【 摘 要 】

We address the problem of spherical deconvolution in a non-parametric statistical framework, where both the signal and the operator kernel are subject to measurement errors. After a preliminary treatment of the kernel, we apply a thresholding procedure to the signal in a second generation wavelet basis. Under standard assumptions on the kernel, we study the minimax performances of the resulting algorithm in terms of L-P losses (p >= 1) on Besov spaces on the sphere. We hereby extend the application of second generation spherical wavelets to the blind spherical deconvolution framework. It is important to stress that the procedure is adaptive with regard to both the target function sparsity and the kernel blurring effect. We end with the study of a concrete example, putting into evidence the improvement of our procedure on the recent blockwise SVD algorithm of Delattre et al. (2012). (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free