Implementing the 2-D Wavelet Transform on SIMD-Enhanced General-Purpose Processors

The 2-D Discrete Wavelet Transform (DWT) consumes up to 68% of the JPEG2000 encoding time. In this paper, we develop efficient implementations of this important kernel on general-purpose processors (GPPs), in particular the Pentium 4 (P4). Efficient implementations of the 2-D DWT on the P4 must address three issues. First, the P4 suffers from a problem known as 64K aliasing, which can degrade performance by an order of magnitude. We propose two techniques to avoid 64K aliasing which improve performance by a factor of up to 4.20. Second, a straightforward implementation of vertical filtering incurs many cache misses. Cache performance can be improved by applying loop interchange, but there will still be many conflict misses if the filter length exceeds the cache associativity. Two methods are proposed to reduce the number of conflict misses which provide an additional performance improvement of up to 1.24. To show that these methods are general, results for the P3 and Opteron are also provided. Third, efficient implementations of the 2-D DWT must exploit the SIMD instructions supported by most GPPs, including the P4, and we present MMX and SSE implementations of horizontal and vertical filtering which provide a maximum speedup of 3.39 and 6.72, respectively.