This paper introduces a new approach to computation of 2-D discrete wavelet transform on modern GPUs. The proposed approach involves block-based processing enabling one seamless transform even for high resolution input data. Inside the blocks, two distinct methods can be used -either separable or non-separable 2-D lifting scheme. Furthermore, the paper presents a comparison of the proposed approach under different conditions to the best existing methods, whereas our approach consistently outperforms the other ones. Our methods are implemented using the OpenCL framework and tested on a wide range GPUs.

With the wide spread of the discrete wavelet transform, the need for its efficient implementation becomes increasingly important. This work presents an improved version of an algorithm suitable to compute the 2-D discrete wavelet transform on GPU. Depending on the GPU platform, it is suitable to split the 2-D transform computation into separated horizontal and vertical passes. Considering the horizontal passes, we have examined and chosen the best performing method among the already known ones. Furthermore, we have adapted this method for an existing algorithm computing the vertical transform pass. This step helps to reduce several synchronizations and arithmetic operations in the utilized computation scheme. For large data, the proposed vertical method achieves speed-up about 30 % compared to the current state of the art methods. In contrast to previously published works, the presented approach is built on the OpenCL parallel programming framework.

In this paper, we introduce several new schemes for calculation of discrete wavelet transforms of images. These schemes reduce the number of steps and, as a consequence, allow to reduce the number of synchronizations on parallel architectures. As an additional useful property, the proposed schemes can reduce also the number of arithmetic operations. The schemes are primarily demonstrated on CDF 5/3 and CDF 9/7 wavelets employed in JPEG 2000 image compression standard. However, the presented method is general, and it can be applied on any wavelet transform. As a result, our scheme requires only two memory barriers for 2-D CDF 5/3 transform compared to four barriers in the original separable form or three barriers in the non-separable scheme recently published. Our reasoning is supported by exhaustive experiments on high-end graphics cards.

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.

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