Simultaneous noise suppression and signal compression using a library of orthonormal bases and the minimum-description-length criterion

Naoki Saito

doi:10.1117/12.170027

15 March 1994 Simultaneous noise suppression and signal compression using a library of orthonormal bases and the minimum-description-length criterion

Naoki Saito

Author Affiliations +

Proceedings Volume 2242, Wavelet Applications; (1994) https://doi.org/10.1117/12.170027
Event: SPIE's International Symposium on Optical Engineering and Photonics in Aerospace Sensing, 1994, Orlando, FL, United States

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.

Citation Download Citation

Naoki Saito "Simultaneous noise suppression and signal compression using a library of orthonormal bases and the minimum-description-length criterion", Proc. SPIE 2242, Wavelet Applications, (15 March 1994); https://doi.org/10.1117/12.170027

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