The Parallel Algorithm for the 2-D Discrete Wavelet Transform

TL;DR

This paper introduces a new parallel algorithm for the 2-D Discrete Wavelet Transform that reduces computational steps, enhancing performance on multi-core processors compared to traditional lifting schemes.

Contribution

The paper proposes a novel rearrangement of calculations in the 2-D DWT to improve parallel processing efficiency on multi-core architectures.

Findings

Outperforms traditional lifting scheme on multi-core CPUs

Reduces number of computational steps in the transform

Demonstrates efficiency on Intel Xeon Phi and Xeon processors

Abstract

The discrete wavelet transform can be found at the heart of many image-processing algorithms. Until now, the transform on general-purpose processors (CPUs) was mostly computed using a separable lifting scheme. As the lifting scheme consists of a small number of operations, it is preferred for processing using single-core CPUs. However, considering a parallel processing using multi-core processors, this scheme is inappropriate due to a large number of steps. On such architectures, the number of steps corresponds to the number of points that represent the exchange of data. Consequently, these points often form a performance bottleneck. Our approach appropriately rearranges calculations inside the transform, and thereby reduces the number of steps. In other words, we propose a new scheme that is friendly to parallel environments. When evaluating on multi-core CPUs, we consistently overcome the original lifting scheme. The evaluation was performed on 61-core Intel Xeon Phi and 8-core Intel Xeon processors.