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Best basis representations with prior statistical models. (English) Zbl 0938.62024

Müller, Peter (ed.) et al., Bayesian inference in wavelet-based models. New York, NY: Springer. Lect. Notes Stat. 141, 155-172 (1999).
Summary: Wavelet packets and local trigonometric bases provide an efficient framework and fast algorithms to obtain a “best representation” of a deterministic signal. Applying these deterministic search techniques to stochastic signals may, however, lead to statistically unreliable results. We revisit this problem and introduce prior models on the underlying signal in noise. We propose several techniques to derive the prior parameters and develop a Bayesian-based approach to the best basis problem. As illustrated by applications to signal denoising, this leads to reduced estimation errors while preserving the classical tree search algorithm.
For the entire collection see [Zbl 0920.00017].

MSC:

62F15 Bayesian inference
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
62P99 Applications of statistics
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems

Software:

WaveLab
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