Estimating deformations of stationary processes

• 成果类型: Article
• 署名作者: Clerc, M; Mallat, S
• 署名单位: Universite Cote d'Azur; Inria; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees; Institut Polytechnique de Paris; Ecole Polytechnique; New York University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2003
• 页码: 1772-1821
• 关键词: texture; shape

摘要

This paper studies classes of nonstationary processes, such as warped processes and frequency-modulated processes, that result from the deformation of stationary processes. Estimating deformations can often provide important information about an underlying physical phenomenon. A computational harmonic analysis viewpoint shows that the deformed autocovariance satisfies a transport equation at small scales, with a velocity proportional to a deformation gradient. We derive an estimator of the deformation from a single realization of the deformed process, with a proof of consistency under appropriate assumptions.