A New Approach of 2-D Discrete Cosine Transform with Moebius Inverse Formula

摘要

The 2-D Discrete Cosine Transform (DCT) is an important mathematical tool in digital image processing and many other fields. This paper is mainly to present an algorithm of 2-D DCT, which turns NxN DCT into N separate 1-D DCT and addition operations, and then to implement DCT with Arithmetic Fourier Transform (AFT), which has been turned out to be an important alternative to the known traditional methods of Fast Fourier Transform (FFT) in terms of accuracy, complexity and speed. The total number of multiplication and addition is only half of that required for the traditional method correspondingly. The simulation results show that this method is feasible and its computational complexity is lower than the row-column algorithm.