A new approach of 2D discrete cosine transform with Mobius inverse formula

The 2D discrete cosine transform (DCT) is an important mathematical tool in digital image processing and many other fields. Our aim is mainly to present an algorithm of 2D DCT, which turns N×N DCT into N separate 1D DCT and addition operations, and then to implement DCT with an arithmetic Fourier transform (AFT), which has 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 multiplications and additions is only half of that required for the corresponding traditional method. Simulation results show that this method is feasible and its computational complexity is lower than the row-column algorithm.