Fast algorithm for the 3D DCT

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