Fast Algorithms for the 2-D Discrete Cosine Transform

Two types of efficient algorithms for fast implementation of the 2-D discrete cosine transform (2-D DCT) are developed. One involves recursive structure which implies that the algorithm for (M/2 X N/2) block be extended to (M X N/2) (M/2 X M) and (M X N) blocks (M and N are integer powers of two). The second algorithm is nonrecursive and therefore it has to be tailored for each block size. Both algorithms involve real arithmetic and they reduce the number of multiplications significantly compared to the fast algorithm developed by Chen et al. [8], while the number of additions remain unchanged.

[1]  C. Smith,et al.  Adaptive Coding of Monochrome and Color Images , 1977, IEEE Trans. Commun..

[2]  F. A. Kamanger.  Interfield hybrid coding of NTSC component video signals , 1980 .

[3]  Nasir Ahmed,et al.  On a Real-Time Walsh-Hadamard/Cosine Transform Image Processor , 1978, IEEE Transactions on Electromagnetic Compatibility.

[4]  J. Makhoul.  A fast cosine transform in one and two dimensions , 1980 .

[5]  Haralick.  A Storage Efficient Way to Implement the Discrete Cosine Transform , 1976, IEEE Transactions on Computers.

[6]  J. Pearl,et al.  Comparison of the cosine and Fourier transforms of Markov-1 signals , 1976 .

[7]  J. Roese,et al.  Interframe Cosine Transform Image Coding , 1977, IEEE Trans. Commun..

[8]  K. R. Rao,et al.  Orthogonal Transforms for Digital Signal Processing , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[9]  M. Narasimha,et al.  Design of a 24-channel transmultiplexer , 1979 .

[10]  A. Ploysongsang,et al.  DCT/DPCM Processing of NTSC Composite Video Signal , 1982, IEEE Trans. Commun..

[11]  M. S. Corrington.  Implementation of fast cosine transforms using real arithmetic , 1978 .

[12]  M. J. Narasimha,et al.  On the Computation of the Discrete Cosine Transform , 1978, IEEE Trans. Commun..

[13]  Hideo Kitajima.  A Symmetric Cosine Transform , 1980, IEEE Transactions on Computers.

[14]  N. Ahmed,et al.  Computation of the discrete cosine transform via the arcsine transform , 1980, ICASSP.

[15]  N. Ahmed,et al.  Discrete Cosine Transform , 1996 .

[16]  P. Camana.  Image processing: Video-bandwidth compression: A study in tradeoffs: In this fledgling field, designers are matching criteria to applications and developing `first-cut¿ hardware , 1979 .

[17]  Richard Jamss Pinnell.  Adaptive Transform Coding of Speech Signals , 1982 .

[18]  K. Sam Shanmugam.  Comments on "Discrete Cosine Transform" , 1975, IEEE Trans. Computers.

[19]  K. R. Rao,et al.  INTERFRAME HYBRID CODING OF NTSC COMPONENT VIDEO SIGNAL. , 1800 .

[20]  Wen-Hsiung Chen,et al.  A Fast Computational Algorithm for the Discrete Cosine Transform , 1977, IEEE Trans. Commun..

[21]  William Kenneth Pratt,et al.  Image transmission techniques , 1979 .

[22]  Meghanad D. Wagh,et al.  A New Algorithm for Discrete Cosine Transform of Arbitrary Number of Points , 1980, IEEE Transactions on Computers.