Accelerating Discrete Wavelet Transforms on Parallel Architectures

TL;DR

This paper introduces non-separable schemes for 2-D discrete wavelet transforms that reduce computational steps and operations, leading to significant performance improvements on GPUs compared to traditional separable methods.

Contribution

It proposes merging separable calculation schemes into non-separable units and an optimization approach, enhancing GPU performance for wavelet transforms.

Findings

Non-separable schemes halve the number of steps compared to separable schemes.

Proposed methods outperform existing schemes on GPU architectures.

Pixel shaders benefit most from the non-separable approach.

Abstract

The 2-D discrete wavelet transform (DWT) can be found in the heart of many image-processing algorithms. Until recently, several studies have compared the performance of such transform on various shared-memory parallel architectures, especially on graphics processing units (GPUs). All these studies, however, considered only separable calculation schemes. We show that corresponding separable parts can be merged into non-separable units, which halves the number of steps. In addition, we introduce an optional optimization approach leading to a reduction in the number of arithmetic operations. The discussed schemes were adapted on the OpenCL framework and pixel shaders, and then evaluated using GPUs of two biggest vendors. We demonstrate the performance of the proposed non-separable methods by comparison with existing separable schemes. The non-separable schemes outperform their separable counterparts on numerous setups, especially considering the pixel shaders.