Max-plus algebra-based wavelet transforms and their applications in compressed image

Max-Plus algebra is one of algebraic structure which only uses two operations maximum and sum, then Max-Plus algebra-based wavelet transforms (MP-wavelets) are wavelet transforms which use operators in Max-Plus algebra. In this paper, we have constructed two types MP-Wavelets that are Type IVa and Type IVb MP-Wavelets. The detail component of the analysis operator of Type IVb MP-Wavelets is defined based on second order backward difference of colors of neighbor pixel. In compressed image, there is no significant difference between Type III and Type IVa but we can see clearly that Type IVa is faster than Type III.