Implementation of 2-D wavelet transform on TESH connected parallel processors

This paper presents the mapping of the 2-D wavelet transform onto a TESH connected multi-processor system. TESH (Tori connected mESHes) is a recently developed interconnection network. Key features of the network are the following: it is hierarchical, thus allowing exploitation of computation locality as well as easy expansion up to a million processors; it permits efficient VLSI/ULSI realization, and appears to be well suited for 3-D VLSI/ULSI implementation. Specifically, the paper develops a parallel algorithm implementation on TESH network, in such a way so as to completely hide the communication overhead. Correspondingly, the system performance is evaluated both for the TESH and for the familiar MESH network with B×B blocks of pixels assigned to each PE, 2J+1 taps per H0 and H1 FIR filters, and S stages of wavelet transform. The time complexity of these two implementations are estimated to be O(B²×J) for both MESH and TESH networks, under the assumption that B=2^S(J+I) for some non-negative integer I. The TESH network has an additional requirement that J⩾2^m·(L-1) where 2^m denotes the size of the Basis Module, and L is the number of levels in TESH´s hierarchy. Thus, the performance of a TESH implemented algorithm is comparable with the MESH based algorithm. However, large TESH networks are easier to implement because of the significantly reduced bisection width compared to large MESH networks