 Application of second generation wavelets to blind spherical deconvolutionT. Vareschi Journal of Multivariate Analysis, 2014, vol. 124, issue C, 398-417 Abstract: 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 Lp 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). Keywords: Blind deconvolution; Blockwise SVD; Spherical deconvolution; Second generation wavelets; Nonparametric adaptive estimation; Linear inverse problems (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:124:y:2014:i:c:p:398-417 Ordering information: This journal article can be ordered from DOI: 10.1016/j.jmva.2013.11.012 Access Statistics for this article Journal of Multivariate Analysis is currently edited by de Leeuw, J. More articles in Journal of Multivariate Analysis from Elsevier |
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