# Accelerating Discrete Wavelet Transforms on GPUs

## TL;DR

This paper introduces a non-separable lifting scheme for 2D discrete wavelet transforms on GPUs, reducing computational steps and outperforming existing methods across various implementations.

## Contribution

It proposes merging horizontal and vertical lifting steps into non-separable units, significantly reducing the number of steps and operations in GPU-based wavelet transforms.

## Key findings

- Non-separable lifting scheme halves the number of steps.
- The scheme outperforms existing methods in many cases.
- Reduces arithmetic operations in wavelet transform computations.

## Abstract

The two-dimensional discrete wavelet transform has a huge number of applications in image-processing techniques. Until now, several papers compared the performance of such transform on graphics processing units (GPUs). However, all of them only dealt with lifting and convolution computation schemes. In this paper, we show that corresponding horizontal and vertical lifting parts of the lifting scheme can be merged into non-separable lifting units, which halves the number of steps. We also discuss an optimization strategy leading to a reduction in the number of arithmetic operations. The schemes were assessed using the OpenCL and pixel shaders. The proposed non-separable lifting scheme outperforms the existing schemes in many cases, irrespective of its higher complexity.

---
Source: https://tomesphere.com/paper/1705.08266