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Scalability of 2-D wavelet transform algorithms: analytical and experimental results on MPPs

This paper studies the scalability of two-dimensional (2-D) discrete wavelet transform (DWT) algorithms on massively parallel processors (MPPs). The principal operation in the 2-D DWT is the filtering operation used to implement the filter banks of the 2-D subband decomposition. This filtering operation can be implemented as a convolution in the time domain or as a multiplication in the frequency domain. We demonstrate that there exist combinations of machine size, image size, and wavelet kernel size for which the time-domain algorithms outperform the frequency domain algorithms and vice-versa. We therefore demonstrate that a hybrid approach that combines time- and frequency-domain approaches can yield linear scalability for a broad range of problem and machine sizes. Furthermore, we show the effect of processor speed versus communication overhead and the use of separable versus nonseparable wavelets on the crossover points between the algorithm approaches.