A Comparison of Real Valued Transforms for Image Compression

Authors: Shivali D. Kulkarni, Ameya K. Naik, Nitin S. Nagori

Abstract:

In this paper we present simulation results for the application of a bandwidth efficient algorithm (mapping algorithm) to an image transmission system. This system considers three different real valued transforms to generate energy compact coefficients. First results are presented for gray scale and color image transmission in the absence of noise. It is seen that the system performs its best when discrete cosine transform is used. Also the performance of the system is dominated more by the size of the transform block rather than the number of coefficients transmitted or the number of bits used to represent each coefficient. Similar results are obtained in the presence of additive white Gaussian noise. The varying values of the bit error rate have very little or no impact on the performance of the algorithm. Optimum results are obtained for the system considering 8x8 transform block and by transmitting 15 coefficients from each block using 8 bits.

Keywords: Additive white Gaussian noise channel, mapping algorithm, peak signal to noise ratio, transform encoding.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1072866

References:

[1] David Salomon, Data Compression - The Complete Reference 3rd Edition, Springer, 2004.
[2] Anil K. Jain. Fundamentals of Digital Image Processing. Prentice-Hall, Inc., 1989.
[3] W. Kou and J. W. Mark, "A new look at DCT-type transforms,"IEEE Trans. Acousr., Speech, Signal Processing, vol. 37, no. 12, pp.1899- 1908, Dec. 1989.
[4] B. G. Lee "A new algorithm to compute the discrete cosine trnsform,", IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-32, pp.1243-1245, Dec. 84.
[5] R. Yip and K. R. Rao, "On the shift property of DCT-s and DST-s," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-35, no.3, pp. 404-406, Mar. 1987.
[6] K. J. Ray Liu and Ching-Te Chiu, "Unified Parallel Lattice Structures for Time-Recursive Discrete Cosine/Sine/Hartley Transforms IEEE Trans. Acousr., Speech, Signal Processing, vol. 41, no. 3, pp.1357-1377, Dec. 1993.
[7] R. Yip and K. R. Rao, "On the computation and effectiveness of discrete sine transform," Comput. Elec. Eng., vol. 7, pp. 45-55, 1980.
[8] S. B. Narayanan and K. M. M. Prabhu, "Fast Hartley transform pruning," IEEE Trans. Signal Processing, vol. 39, no. 1, pp. 230- 233, Jan. 1991.
[9] H. M. Behairy and M. S. Khorsheed, "Improving Image Quality in Remote Sensing Satellites using Channel Coding," Proceedings of World Academy of Science, Engineering and Technology, vol. 9, pp. 189-194, Nov. 2005.
[10] J. G. Proakis, Digital Communications, 4th ed., McGraw-Hill, New York, 2001, pp. 254-839.