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Abstract:
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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. Results from numerical experiments suggest that our algorithms produce favorite results when comparing to several common methods. To illustrate the flexibility of our approach, examples with Poisson data smoothing and image denoising are also provided.
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