Discrete fractal step multiwavelets and multiwavelet packets – a new multiwavelet technology for image processing and coding

Abstract

The construction method and algorithms of twodimension discrete fractal step multiwavelets and multiwavelet packets, discrete multiwavelet-transforms with multiwavelet packets of given sizes for different levels of the schedule without performing convolution and sample thinning operations, unlike the classical method, have been developed. Algorithms of 2D fast multiwavelet transforms (FMWT) with multiwavelet packets of given sizes for various levels of the low computational complexity decomposition have been developed. The method and algorithms of image coding based on 2D FMWT as a new multiwavelet technology are proposed. A method of image coding based on a three-level 2D FMWT is proposed, which, compared to the well-known classic Malla algorithm, has 78.8 times less multiplicative complexity and requires 22.5 times less additions.