MDL denoising

'The so-called denoising problem, relative to normal models for noise, is formalized such that "noise" is defined as the incompressible part in the data while the compressible part defines the meaningful information-bearing signal. Such a decomposition is effected by minimization of t...

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Bibliographic Details
Published in:IEEE transactions on information theory 2000-11, Vol.46 (7), p.2537-2543
Main Author: Rissanen, J.
Format: Article
Language:English
Subjects:
Computer programming
Mathematical analysis
Mathematical models
Matrix
Minimization
Minimization methods
Noise
Optimization
Regression
Stochastic models
Vectors (mathematics)
Wavelet transforms
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Summary:'The so-called denoising problem, relative to normal models for noise, is formalized such that "noise" is defined as the incompressible part in the data while the compressible part defines the meaningful information-bearing signal. Such a decomposition is effected by minimization of the ideal code length, called for by the minimum description length (MDL) principle, and obtained by an application of the normalized maximum-likelihood technique to the primary parameters, their range, and their number. For any orthonormal regression matrix, such as defined by wavelet transforms, the minimization can be done with a threshold for the squared coefficients resulting from the expansion of the data sequence in the basis vectors defined by the matrix.
ISSN:0018-9448
1557-9654
DOI:10.1109/18.887861