Reducing 3D Fast Wavelet Transform Execution Time Using Blocking and the Streaming SIMD Extensions

Abstract

The video compression algorithms based on the 3D wavelet transform obtain excellent compression rates at the expense of huge memory requirements, that drastically affects the execution time of such applications. Its objective is to allow the real-time video compression based on the 3D fast wavelet transform. We show the hardware and software interaction for this multimedia application on a general-purpose processor. First, we mitigate the memory problem by exploiting the memory hierarchy of the processor using several techniques. As for instance, we implement and evaluate the blocking technique. We present two blocking approaches in particular: cube and rectangular, both of which differ in the way the original working set is divided. We also put forward the reuse of previous computations in order to decrease the number of memory accesses and floating point operations. Afterwards, we present several optimizations that cannot be applied by the compiler due to the characteristics of the algorithm. On the one hand, the Streaming SIMD Extensions (SSE) are used for some of the dimensions of the sequence (y and time), to reduce the number of floating point instructions, exploiting Data Level Parallelism. Then, we apply loop unrolling and data prefetching to specific parts of the code. On the other hand, the algorithm is vectorized by columns, allowing the use of SIMD instructions for the y dimension. Results show speedups of 5x in the execution time over a version compiled with the maximum optimizations of the Intel C/C++ compiler, maintaining the compression ratio and the video quality (PSNR) of the original encoder based on the 3D wavelet transform. Our experiments also show that, allowing the compiler to perform some of these optimizations (i.e. automatic code vectorization), causes performance slowdown, demonstrating the effectiveness of our optimizations.

The 2D wavelet transform on emerging architectures: GPUs and multicores

“…Today, the standard MPEG-4 [23][24] supports an ad-hoc tool for encoding textures and still images, based on a wavelet algorithm. In a previous work [25], we have presented the implementation of a lossy encoder for medical video based on the 3D fast wavelet transform. This encoder achieves both high compression ratios and excellent quality, so that medical doctors can not find longer differences between the original and the reconstructed video.…”

Exploiting Varying Resource Requirements in Wavelet-based Applications in Dynamic Execution Environments

“…Meerwald et al [12], Bernabe et al [13], Chrysafis and Ortega [14] and Lafruit et al [15] present different memory-optimized execution orders or localizations of the WT, offering various methods to avoid off-chip misses: [12] reduces conflict misses in the vertical WT filtering by modifying the data layout and improves the spatial locality by modifying the execution order. Bernabe et al [13] reduces the cache misses during vertical filtering by computing tiles of merged horizontal and vertical filtering, [14] further avoids misses during the higher WT levels by merging lines of computation over all the WT levels, while [15] offers the same advantages, but by merging in a block-based manner, which corresponds well to further processing blocks.…”

“…Bernabe et al [13] reduces the cache misses during vertical filtering by computing tiles of merged horizontal and vertical filtering, [14] further avoids misses during the higher WT levels by merging lines of computation over all the WT levels, while [15] offers the same advantages, but by merging in a block-based manner, which corresponds well to further processing blocks. Chaver et al [16] finally realizes a trade-off between the in-placing freedom and spatial locality present in certain implementation styles of the WT.…”

Optimizing Gaussian filtering of volumetric data using SSE

“…SIMD extensions of the instruction sets are successfully used in 3D as well. For example, [41] describes the SIMD optimization of 3D wavelet transform. Tomographic reconstruction can be sped up by a factor of 3 using SSE, as described in [42].…”