Directionlet transform based on GPU

Directionlet transform belongs to third generation wavelet transform and it has been widely applied in many fields like image processing, fault diagnosis, medical imaging and so on. Although the separability, second sampling, the simplicity of calculation and design of the filter of the two-dimensional wavelet transform filter are preserved in directionlet transform, there also exists a problem of computing speed, that is, it would cost too much time when the test data is large. To solve the problem mentioned above, an efficient parallel algorithm based on the Graphics Processor Unit (GPU) using the Compute Unified Device Architecture (CUDA) is proposed in this paper. Firstly, the test images are decomposed into two cosets according to the generator matrix. Then the cosets are restored to normal matrixes by matrix transposition. Finally, we take the unequal number of one-D WT along the transform direction and queue direction to complete the directionlet transform. Besides, we use the shared memory and constant memory inside GPU to speed up the algorithm, that is achieving the parallelization. A group of images with different size are tested in the experiment before we draw a conclusion. The speed-up ratio of the parallel algorithm of directionlet transform based on GPU is about five to ten times than that on CPU. Thus, this algorithm can reduce running time significantly.