GPU Accelerated Randomized Singular Value Decomposition and Its Application in Image Compression

In this paper, we present a GPU-accelerated implementation of randomized Singular Value Decomposition (SVD) algorithm on a large matrix to rapidly approximate the top-k dominating singular values and correspondent singular vectors. The fundamental idea of randomized SVD is to condense a large matrix into a small dense matrix by random sampling while keeping the important information. Then performing traditional deterministic SVD on this small dense matrix reveals the topk dominating singular values/singular vectors approximation. The randomized SVD algorithm is suitable for the GPU architecture; however, our study finds that the key bottleneck lies on the SVD computation of the small matrix. Our solution is to modify the randomized SVD algorithm by applying SVD to a derived small square matrix instead as well as a hybrid GPU-CPU scheme. Our GPU-accelerated randomized SVD implementation is around 6~7 times faster than the corresponding CPU version. Our experimental results demonstrate that the GPU-accelerated randomized SVD implementation can be effectively used in image compression.