Two-Dimensional Discrete Wavelet Transform on Large Images for Hybrid Computing Architectures: GPU and CELL

Abstract

Abstract. The Discrete Wavelet Transform (DWT) has gained the momentum in signal processing and image compression over the last decade bringing the concept up to the level of new image coding standard JPEG2000. Thanks to many added values in DWT, in particular inherent multi-resolution nature, wavelet-coding schemes are suitable for various applications where scalability and tolerable degradation are relevant. Moreover, as we demonstrate in this paper, it can be used as a perfect benchmarking procedure for more sophisticated data compression and multimedia applications using General Purpose Graphical Processor Units (GPGPUs). Thus, in this paper we show and compare experiments performed on reference implementations of DWT on Cell Broadband Engine Architecture (Cell B.E) and nVidia Graphical Processing Units (GPUs). The achieved results show clearly that although both GPU and Cell B.E. are being considered as representatives of the same hybrid architecture devices class they di er greatly in programming style and optimization techniques that need to be taken into account during the development. In order to show the speedup, the parallel algorithm has been compared to sequential computation performed on the x86 architecture.

Block-Based Approach to 2-D Wavelet Transform on GPUs

“…Their fastest implementation uses the coalesced memory access. In [1], the authors calculate the wavelet transform through 4 kernels. The first kernel performs an image transposition using work groups of size 16 × 16 threads, where the thread processes one image element.…”

“…In [3] and [1], data transposition was performed in between the horizontal and vertical series of 1-D transforms. In [11] and [12], Tenllado et al adapted the discrete wavelet transform on GPU fragment shaders.…”

“…The row-column method applied on the entire 2-D image was used for instance in [11], [12], [3], [1], [4], [5]. In [3] and [1], data transposition was performed in between the horizontal and vertical series of 1-D transforms.…”

“…1 OpenCL is a framework for general-purpose parallel programming across multiple device types. In this framework, a platform independent executable program is called the kernel.…”

Parallel wavelet schemes for images

“…The row-column methods process all of the horizontal filtering steps prior to the vertical ones. The row-column method applied on the entire 2-D image was used for instance in [10][11][12][13][14][15][16]. In some papers, the transition between the horizontal and vertical stage is accompanied with data transposition.…”