The data compression book (2nd ed.)
The data compression book (2nd ed.)
Recognizable Sets with Multiplicities in the Tropical Semiring
MFCS '88 Proceedings of the Mathematical Foundations of Computer Science 1988
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Fuzzy relation equations for coding/decoding processes of images and videos
Information Sciences—Informatics and Computer Science: An International Journal
Fuzzy Optimization and Decision Making
Compression and decompression of images with discrete fuzzy transforms
Information Sciences: an International Journal
Dioïds and semirings: Links to fuzzy sets and other applications
Fuzzy Sets and Systems
A novel secret image sharing scheme in color images using small shadow images
Information Sciences: an International Journal
Joint coding and embedding techniques for multimedia images
Information Sciences: an International Journal
Improved batch fuzzy learning vector quantization for image compression
Information Sciences: an International Journal
Multiresolution image representation using combined 2-D and 1-D directional filter banks
IEEE Transactions on Image Processing
A motion compression/reconstruction method based on max t-norm composite fuzzy relational equations
Information Sciences: an International Journal
IEEE Transactions on Fuzzy Systems
Direction-Adaptive Discrete Wavelet Transform for Image Compression
IEEE Transactions on Image Processing
A novel max-plus algebra based wavelet transform and its applications in image processing
SMC'09 Proceedings of the 2009 IEEE international conference on Systems, Man and Cybernetics
Fuzzy transforms for compression and decompression of color videos
Information Sciences: an International Journal
Invertible matrices and semilinear spaces over commutative semirings
Information Sciences: an International Journal
Information Sciences: an International Journal
Information Sciences: an International Journal
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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.