2007/01/06 by Thomas C. M. Lee, Xiao-Li Meng, Xiao‐Li Meng +2
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Image and Signal Denoising Methods #Sparse and Compressive Sensing Techniques #Statistical and numerical algorithms #Statistics Theory (math.ST) #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.math/0701196
arxiv created 2007/01/06 · openalex publication_date 2007/01/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Inspired by the key principle behind the EM algorithm, we propose a general methodology for conducting wavelet estimation with irregularly-spaced data by viewing the data as the observed portion of an augmented regularly-spaced data set. We then invoke the self-consistency principle to define our wavelet estimators in the presence of incomplete data. Major advantages of this approach include: (i) it can be coupled with almost any wavelet shrinkage methods, (ii) it can deal with non--Gaussian or correlated noise, and (iii) it can automatically handle other kinds of missing or incomplete observations. We also develop a multiple-imputation algorithm and fast EM-type algorithms for computing or approximating such estimates. Results from numerical experiments suggest that our algorithms produce favorite results when comparing to several common methods, and therefore we hope these empirical findings would motivate subsequent theoretical investigations. To illustrate the flexibility of our approach, examples with Poisson data smoothing and image denoising are also provided.