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There is now a CONTENT FREEZE for Mercury while we switch to a new platform. It began on Friday, March 10 at 6pm and will end on Wednesday, March 15 at noon. No new content can be created during this time, but all material in the system as of the beginning of the freeze will be migrated to the new platform, including users and groups. Functionally the new site is identical to the old one. webteam@gatech.edu
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We propose a general methodology for conducting wavelet estimation with irregularly-spaced data by viewing them 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. (This is joint work with Thomas Lee of Colorado State University.)
