Data Compression Using New Fast Adaptive Cosine-Haar Transforms

Fast algorithms used to calculate sequences of adaptive Fourier?Haar and consequently Cosine?Haar transforms are defined. The transforms are constructed in such a way as to achieve maximum possible compression of multidimensional signals. The influence of the transform degree of both classical and adaptive Cosine?Haar transforms on the compression efficiency is studied. This allows us to optimize the compression quality and thus the computational complexity with respect to the transform degree.

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

[2]  Vladimir Britanak,et al.  A unified discrete cosine and discrete sine transform computation , 1995, Signal Process..

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

[4]  N. Ahmed,et al.  FAST TRANSFORMS, algorithms, analysis, applications , 1983, Proceedings of the IEEE.

[5]  H. Kitajima.  Energy Packing Efficiency of the Hadamard Transform , 1976, IEEE Trans. Commun..

[6]  H. Nussbaumer.  Fast Fourier transform and convolution algorithms , 1981 .

[7]  William C. Miller,et al.  On Computing the Discrete Cosine Transform , 1978, IEEE Transactions on Computers.

[8]  M. A. Narasimhan,et al.  Complex Haar transform , 1974 .

[9]  Vladimir Britanak.  On the discrete cosine transform computation , 1994, Signal Process..

[10]  C. K. Yuen,et al.  Walsh Functions and Their Applications , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

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

[12]  E. O. Brigham,et al.  The Fast Fourier Transform , 1967, IEEE Transactions on Systems, Man, and Cybernetics.