LOCALIZED SPHERICAL DECONVOLUTION

• 成果类型: Article
• 署名作者: Kerkyacharian, Gerard; Thanh Mai Pham Ngoc; Picard, Dominique
• 署名单位: Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/10-AOS858
• 发表日期: 2011
• 页码: 1042-1068
• 关键词: INVERSE PROBLEMS; needlets

摘要

We provide a new algorithm for the treatment of the deconvolution problem on the sphere which combines the traditional SVD inversion with an appropriate thresholding technique in a well chosen new basis. We establish upper bounds for the behavior of our procedure for any L-p loss. It is important to emphasize the adaptation properties of our procedures with respect to the regularity (sparsity) of the object to recover as well as to inhomogeneous smoothness. We also perform a numerical study which proves that the procedure shows very promising properties in practice as well.