Lossless image compression using wavelets over finite rings and related architectures
Andreas Klappenecker, Frank U. May, Armin Nueckel · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1997
In this paper we give a brief introduction to filter banks over commutative rings. In contrast to filter banks over the real numbers, we employ finite ring arithmetic to control the number of bits in the signal representations. This way we avoid the coefficient swell problem that is preeminent in rings of characteristic zero. We derive decompositions for images that are tailored to dedicated hardware implementations. These decompositions reduce the size of line-buffers which dominate the silicon area in integrated circuit implementations. As an application, we derive a lossless compression scheme for 8 bit monochrome images using wavelet filters with values in the ring Z/256Z.