A statistical analysis of the kernel-based MMSE estimator with application to image reconstruction
作者:
Highlights:
• We develop a statistical analysis of the kernel-based minimum mean square error (KMMSE) estimator with emphasis in locally linear functions.
• Two error risk measures are proposed for this case.
• We show that KMMSE with a suitable bandwidth estimation procedure provides an approximation to sparse linear prediction with a bias correction term.
• For the case of recursive estimation (as it is commonly used in image reconstruction), the propagation error is also assessed through a vector Taylor series expansion.
• The MSE and propagation error measures previously proposed are applied to a novel filling ordering procedure.
摘要
•We develop a statistical analysis of the kernel-based minimum mean square error (KMMSE) estimator with emphasis in locally linear functions.•Two error risk measures are proposed for this case.•We show that KMMSE with a suitable bandwidth estimation procedure provides an approximation to sparse linear prediction with a bias correction term.•For the case of recursive estimation (as it is commonly used in image reconstruction), the propagation error is also assessed through a vector Taylor series expansion.•The MSE and propagation error measures previously proposed are applied to a novel filling ordering procedure.
论文关键词:Recursive signal reconstruction,Multivariate kernel-based regression and estimation,Sparse linear prediction,Minimum mean square error estimation,Image/video error concealment,Filling ordering
论文评审过程:Received 28 October 2016, Revised 22 March 2017, Accepted 22 March 2017, Available online 27 March 2017, Version of Record 5 April 2017.
论文官网地址:https://doi.org/10.1016/j.image.2017.03.015