A Novel Low-Complexity and Parallel Algorithm for DCT IV Transform and Its GPU Implementation

Abstract

This study proposes a novel factorization method for the DCT IV algorithm that allows for breaking it into four or eight sections that can be run in parallel. Moreover, the arithmetic complexity has been significantly reduced. Based on the proposed new algorithm for DCT IV, the speed performance has been improved substantially. The performance of this algorithm was verified using two different GPU systems produced by the NVIDIA company. The experimental results show that the novel proposed DCT algorithm achieves an impressive reduction in the total processing time. The proposed method is very efficient, improving the algorithm speed by more than 4-times—that was expected by segmenting the DCT algorithm into four sections running in parallel. The speed improvements are about five-times higher—at least 5.41 on Jetson AGX Xavier, and 10.11 on Jetson Orin Nano—if we compare with the classical implementation (based on a sequential approach) of DCT IV. Using a parallel formulation with eight sections running in parallel, the improvement in speed performance is even higher, at least 8.08-times on Jetson AGX Xavier and 11.81-times on Jetson Orin Nano.