Simultaneous noise suppression and signal compression using a library of orthonormal bases and the minimum description length criterion,
in Wavelets in Geophysics (E. Foufoula-Georgiou and P. Kumar, eds.),
Chap. XI, pp. 299-324, Academic Press, San Diego, CA, 1994.
Abstract
We describe an algorithm to estimate a discrete signal from
its noisy observation, using a library of orthonormal bases
(consisting of various wavelets, wavelet packets, and local trigonometric
bases) and the information-theoretic criterion called minimum description
length (MDL). The key to effective random noise suppression is that
the signal component in the data may be represented efficiently by one or more
of the bases in the library, whereas the noise component cannot be represented
efficiently by any basis in the library.
The MDL criterion gives the best compromise between the fidelity of the
estimation result to the data (noise suppression)
and the efficiency of the representation of the estimated signal
(signal compression): it selects the "best" basis and the "best"
number of terms to be retained out of various bases in the library in an
objective manner.
Because of the use of the MDL criterion, our algorithm is free from any
parameter setting or subjective judgments.
This method has been applied usefully to various geophysical datasets
containing many transient features.
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