Research interests are moslty connected with analysis, approximation and compression of signals of various nature with the aid of fractal, wavelet and related methods. Have developed a method of approximation of functions of one real variable (as well as time series) by fractal functions (sequences), based on localization of the strongest Holder singularities. This technology was also applied to fractal modeling of financial time series. Have developed several compression methods for information arrays generated in computational modeling and computer graphics: approximation of the computed fields with the aid of Chebyshev, wavelet and multiwavelet expansions, compression of digital images with the aid of local palletizing and adaptive partitioning of image blocks into color clusters. Have developed a method for fast information search on nonregular planar and spatial grids. Have developed (in co- authorship) several formats for 3D models and scenes representation, to be used in the new version of multimedia format MPEG4, which is currently under development.
Main publications:
Levkovich-Maslyuk L. I. Wavelet-based determination of generating matrices for fractal interpolation functions // Regular and Chaotic Dynamics, 1998, 3(2), 20–29.
Levkovich-Maslyuk L. I. Determination of the scaling parameters of affine fractal interpolation functions with the aid of wavelet analysis // SPIE Proceedings, v. 2825, paper 2825-91, 1996.
Levkovich-Maslyuk L. I. Wavelet analysis and its applications to time series // NATO Advanced Studies Institute (ASI), "Nonlinear Dynamics in Life and Social Sciences" (Moscow, Russia), 2001.
Levkovich-Maslyuk L. I., Zhirkov A., Kalyuzhny P. Texture compression with adaptive block partitions // Proceedings of 8th ACM International Conference on Multimedia "Multimedia 2000", Los Angeles, USA.
