### Subiono, Mahmud Yunus : *COMPUTATION DECOMPOSITION HAAR WAVELET BASED MAX-PLUS ALGEBRA*

Dr. Drs. Mahmud Yunus M.Si.

The International Conference on Numerical Analysis and Optimization (ICeMATH 2011), di Universitas Ahmad Dahlan Yogyakarta Indonesia, 6-8 Juni 2011.

wavelet transform; wavelet morphology; max-plus algebra.

Abstract

In this paper, the formula a wavelet transform max-plus is proposed, which
is a wavelet transform to compute coefficients of decomposition in max-plus algebra
system. This wavelet transform is proposed by simplifying the morphological wavelet
transform. It is a very reasonable thing to do because in max-plus algebra system, where
analysis and synthesis operation are defined by max and standard sum, so that, can
minimize a complexity in a calculation, therefore, they are can ensure a data information.
The operators that used in max-plus algebra system are closely related to operators in
mathematical morphology, such as dilation and erosion, used to formulate the wavelet
transform morphology. The formulation of this transformation will be used for
decompositioning of a higher-resolution signal into a lower-resolution signals. A
recursive wavelet transform, will decompose a signal into an approximation signal (low
frequency part) and some detail signal (high frequency part). We will also be
development an algorithm for computing coefficients of decomposition in max-plus
algebra system