Efficient estimation of a density in a problem of tomography

• 成果类型: Article
• 署名作者: Cavalier, L
• 署名单位: Aix-Marseille Universite
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1016218233
• 发表日期: 2000
• 页码: 630-647
• 关键词: INVERSE PROBLEMS

摘要

The aim of tomography is to reconstruct a multidimensional function From observations of its integrals over hyperplanes. We consider the model that corresponds to the case of positron emission tomography. We have n i.i.d. observations from a probability density proportional to Rf, where Rf stands for the Radon transform of the density f. We assume that f is an N-dimensional density such that its Fourier transform is exponentially decreasing. We find an estimator of f which is asymptotically efficient; it achieves the optimal rate of convergence and also the best constant for the minimax risk.