Use of hybrid method in wavelets base selection for signal compression

Kalle Saastamoinen; Jouni Sampo

doi:10.1117/12.504418

28 January 2004 Use of hybrid method in wavelet base selection for signal compression

Kalle Saastamoinen, Jouni Sampo

Proceedings Volume 5208, Mathematics of Data/Image Coding, Compression, and Encryption VI, with Applications; (2004) https://doi.org/10.1117/12.504418
Event: Optical Science and Technology, SPIE's 48th Annual Meeting, 2003, San Diego, California, United States

Abstract

In this paper we study a problem of signal compression how to choose a best mother wavelet from the set S of wavelets. The approach is following: First we calculate a discrete wavelet transform of signal by using one standard wavelet. Then we form coefficients m_i for each scale i from the wavelet expansions coefficients. Coefficients m_i are used for selecting best wavelet from the set S. Selection is classification problem and we have constructed classification algorithm that uses fuzzy similarity that is based on a continuous t-norm called Lukasiewicz algebra. We are using normal and cumulative forms of generalized Lukasiewicz algebra and we have also applied a genetic algorithm into the our classifier to choose appropriate weights in our classification tasks. There are many advantages what we get by using t-norm called Lukasiewicz in classification: 1) Structure has a promising mathematical background 2) Mean of many fuzzy similarities is still a fuzzy similarity 3) Any pseudo-metric induces fuzzy similarity on a given non-empty set X with respect to the Lukasiewicz-conjunction. Algorithm is efficient especially because we have to calculate wavelet transform only once and classification is simple and fast. Algorithm is also very flexible, cause we can implement any type metrics or mean measures into it. As our results we will present a new method to select best mother wavelet from a given set S. We will also show that proposed hybrid method can be used in this kind of analytical problems. The best way to form coefficients m_i and choose metric or measure is depended of class of signals we are working with, which is still unclear.

Citation Download Citation

Kalle Saastamoinen and Jouni Sampo "Use of hybrid method in wavelet base selection for signal compression", Proc. SPIE 5208, Mathematics of Data/Image Coding, Compression, and Encryption VI, with Applications, (28 January 2004); https://doi.org/10.1117/12.504418

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