Parallelization of Wavelet Filters Using Simd Extensions

Abstract

Much work has been done to optimize wavelet transforms for SIMD extensions of modern CPUs. However, these approaches are mostly restricted to the vertical part of 2-D transforms with line-wise organized memory layouts because this leads to a rather straight forward SIMD-implementation. This work shows for an example of a common wavelet filter new approaches to use SIMD operations on 1-D transforms that are able to produce reasonable speedups. As a result, the performance of algorithms that use wavelet transforms, such as JPEG2000, can be increased significantly. Various variants of parallelization are presented and compared. Their advantages and disadvantages for general filters are discussed.

Short-Vector SIMD Parallelization in Signal Processing

“…Also, approaches on old SIMD arrays [12,13,14] cannot be adapted directly. Therefore, good manual vectorization strategies [15,16] are important.…”

Parallelization of IIR filters using SIMD extensions

“…In [4], [5], it turned out that the performance of an implementation of a filtering algorithm possibly depends on whether the signal data is in the cache or not. The method to find this out is to vary the data length and to repeat the filtering several times.…”

“…The parallelization of FIR filters has been investigated thoroughly, especially for wavelet filters, for old SIMD arrays [1], [2], [3] and SIMD extensions of modern general purpose processors in the 1-D case [4], [5] and the 2-D case [6], [7], [8]. The parallelization of IIR filters is more difficult due to data dependencies.…”

“…In the FIR case, iterations of the outer loop, i.e. entire inner loops, are independent of each other, leading to a rather straightforward SIMD parallelization where the two loops (inner and outer) are interchanged for a number of outer iterations equal to the SIMD vector size p. See [4], [5] and Fig. 1(a).…”