On the scalability of 2-D wavelet transform algorithms on fine-grained parallel machines

We study the scalability of 2-D discrete wavelet transform algorithms on fine-grained parallel architectures. The principal operation in the 2-D DWT is the filtering operation used to implement the filter banks of the 2-D subband decomposition. We demonstrate that there exist combinations of the machine size, image size, and wavelet size for which the time-domain algorithms outperform the frequency domain algorithms, and vice-versa. We, therefore, demonstrate that a hybrid approach which combines time- and frequency-domain approaches can yield optimal performance for a broad range of problem and machine sizes. Furthermore, we show the effect of processor speed and the use of separable versus nonseparable wavelets on the crossover points between the algorithm approaches.