Max-plus algebra-based wavelet transforms and their FPGA implementation for image coding

In the present paper, we propose new image coding methods based on max-plus algebra-based wavelet transforms (MP-Wavelets). Max-plus algebra is an algebraic structure on the set of integers, endowed with maximum, minimum and standard addition as operations. The proposed wavelet decomposition schemes are novel classes of morphological wavelets which, in contrast to the existing approaches, involve only integers and only max, min and addition in their computation. Since they do not involve floating point calculations and multiplications, MP-Wavelets have a very low computational complexity and they are suitable for efficient hardware implementation. Through image coding experiments using 10,000 images extracted from low resolution web-crawled misc database, the characteristics of the proposed MP-Wavelets are presented. Furthermore, we show a computational complexity analysis to compare MP-Wavelets to one of the fastest wavelet transforms, the conventional Haar wavelet. The applicability of MP-Wavelets in video coding is also confirmed by image coding experiments using residual frames. Finally, the field programmable gate arrays (FPGA) implementation of MP-Wavelets is presented to confirm suitability of MP-Wavelets for hardware implementation.