Orthonormalized basic of fractal stepped multiwavelets – a new multiwavelet technology for signal and image processing

Fìz.-mat. model. ìnf. tehnol. 2021, 32:91-95

Abstract

A new class of fractal step functions with linear and nonlinear changes in values is described, and on their basis a recurrent method for constructing functions of a new class of fractal step multiwavelets (FSMW) of various shapes with linear and nonlinear changes in values is developed. A method and an algorithm for constructing a whole family of basic FSMW systems have been developed. An algorithm for calculating the coefficients of a discrete multiwavelet transform based on a multiwavelet packet without performing convolution and decimated sampling operations, in contrast to the classical method, is presented. A method and algorithm for fast multiwavelet transform of low computational complexity has been developed, which, in comparison with the well-known classical Mall's algorithm, is 70 times less in multiplicative complexity, and 20 times less in additive complexity.

References

1. Martin, M. B., Bell, A. E. (2001). New image compression techniques using multiwavelets and multiwavelet packets. IEEE Trans Image Process, 10(4), 500-510.
   DOI doi.org/10.1109/83.913585
2. Hnativ, L. O. (2007). New orthonormal basis for the step wavelet system. VI Int. scientific and technical conf. "Gyrotechnology, navigation, motion control and design of aerospace technology", Kyiv, April 26-27. Sat. add. P.II. Kyiv: NTUU "KPI".
3. Hnativ, L. O. (2007). Methods for constructing orthonormal basis wavelet systems based on step functions. Etc. international symp. "Questions of optimization of calculations (POO-XXKIIII)", Ukraine, Crimea, town. Katsiveli, September 23-28.
4. Hnativ, L. O. (2015). A method for constructing a family of orthonormal basis systems of fractal multiwavelets based on step functions. Etc. Int. shk. "Questions of optimization of calculations (POO-XLII), Ukraine, Zakarpattya region, Chinadievo town, 21-25 September.
5. Hnativ, L. O. (2017). Fractal stepped multiwavelets are a new wavelet technology for signal processing and image encoding. Abstracts Int. sciences. conf. "Modern informatics: problems, achievements and ...", Ukraine, Kyiv, December 13-15.
6. Malla, C. (2005). Wavelets in signal processing. Moskva: Myr.