Fast algorithm for the 3D DCT

The three-dimensional discrete cosine transform (3D DCT) has been used in many 3D applications such as video coding and compression. Many fast algorithms have been developed for the calculation of the 1D DCT. These algorithms are then used for the calculation of the 3D DCT using the row-column approach. However, 3D algorithms involve fewer arithmetic operations and can be faster. The 3D decimation-in-frequency vector-radix algorithm (3D DIF VR), for the 3D DCT-II, is developed and its arithmetic complexity analysed and compared to similar algorithms. In comparison with the familiar row-column approach, the 3D vector-radix reduces the number of multiplications significantly while keeping the number of additions the same and hence can be used for fast 3D image and video coding and compression