IJPAM: Volume 64, No. 4 (2010)

1D AND 2D HAAR TRANSFORM AND PARALLEL
IMPLEMENTATION IN NOTHING SHARE ARCHITECTURE

Jaumin Ajdari
Information and Communication Technology Research and Training Centre
South-East European University
Tetovo, 1220, MACEDONIA
e-mail: [email protected]


Abstract.Wavelets transform, particularly the discrete wavelet transform (DWT) is an important problem for many applications. This paper describes the 1D and 2D sequential and parallel implementation of the simplest wavelet transform, namely the Haar transform. We have described the mathematical theory of Haar transformation and algorithmic implementation of their computations. From the mathematical theory we have defined the 1D and 2D Haar transformation and we have also shown some important results which we use for their computations. From the algorithmic implementation we have done the 1D and 2D sequential and parallel implementation and for the 2D parallel implementation we propose several types of parallelization, like the parallelization on mesh and non mesh architecture. Parallel implementations are done based on the nothing share computer system architecture and the MPI programming paradigm. We also analyze their complexity and show that the complexity of parallel implementation depends on the number of processes and on the number of real processing units used for process mapping.

Received: October 9, 2010

AMS Subject Classification: 68W10

Key Words and Phrases: multiresolutional analyses, Haar transform, sequential transform, parallel transform

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 64
Issue: 4