Open Access Open Access  Restricted Access Subscription or Fee Access

Image Representation by First Generation Wavelets and Its Application to Compression

M. Santhosh, B. Stephen Charles, M. N. Giri Prasad

Abstract


Image is a two dimensional plot of intensity information. A digital image is a collection of numbers representing the intensity values. The digital image is stored primarily as a matrix (more specifically as an array of multi-dimension). Hence the processing of the image is done primarily on this representation of the image. Because this representation is a raw data of pixels and distributed along the plane non-uniformly, one cannot apply any operation more effectively. The aim of this paper is to analyze the wavelet representation of an image. In this paper, the representation of image by wavelets is presented and verified the effectiveness of the representation by performing compression on the new representation. This paper proposes a new composite design metric to analyze image compression. The first generation wavelets Haar, Daubechies, Bioorthogonal, Coiflet, Symlet and Di-Meyer are considered. The work was tested on a large number of images and the results are presented.

Keywords


Image Representation, Wavelet, Compression, SPIHT

Full Text:

PDF

References


S. Mallat, “A Theory for Multiresolution Signal Decomposition: The Wavelet Representation," IEEE Pattern Analysis and Machine Intelligence, vol. 11, no. 7, pp. 674{693, 1989.

L.Szu Y.Sheng, “Wavelet processing and optics”, IEEE 84(5), 1996, pp. 720–732 Imaging, October 1999, Vol.7 (4).

M.Borland, “Wavelet in image communication”, Elsevier 1994.

Charles Hsu et al., 1999, “Wavelet brass boards for live video via ratio”, Journal of Electronic Imaging, Vol. 7(4).

O.Strome et al, 1997, “Study of wavelet decompositions for image/video compression by software codecs”, IEEE, pp. 125–132.

G. Piella, H.J.A.M. Heijmans “Adaptive lifting scheme with perfect reconstruction”, IEEE Trans. on Signal Processing, Vol.50 (7), July 2002, pp. 1620–1630.

G. Piella, B. Pesquet-Popescu, H.J.A.M. Heijmans, 2002, “Adaptive update lifting with a decision rule based on derivative filters”, IEEE Signal Processing Letters, Vol.9 (10).

K. A. Kotteri, A. E. Bell, and J. E. Carletta, “Design of multiplierless, high-performance, wavelet filter banks with image compression applications,” IEEE Tran. On Circuits and Systems-I, vol. 51, no. 3, pp. 483.494, Mar. 2004.

Said, A. and Pearlman, W. A., “A New, Fast, and Efficient Image Codec Based on Set Partitioning in Hierarchical Trees,” IEEE Trans. CSVT, vol. 6, no. 3, June 1996, pp. 243-250,

Shapiro JM. Embedded image coding using zero trees of wavelets coefficients. IEEE Transactions on Signal Processing 1993; 41:3445–62.

Daubechies, I. "Ten Lectures on Wavelets, SIAM", 1992.

R.R. Coifman and M.V.Wickerhauser, “Entropy Based Algorithm for Best Basis Selection”, IEEE Trans. Inform. Therory, vol. 38, pp.713-718, March 1992.

Meyer FG, Averbuch AZ, Stromberg JO. "Fast adaptive wavelet packet image compression". IEEE Transactions on Image Processing 2000; 9:792–800.

G.Wallace, “The JPEG still picture compression standard”, IEEE TCE, 38, 1992.

Independent JPEG Group, version 6a:http://www.ijg.org.

G. K. Wallace, “The JPEG still picture compression standard”, in IEEE Transactions on Circuits and Systems for Video Technology, vol. 6, June 1996.

O. K. Al-Shaykh, “JPEG-2000: A new still image compression standard”, in Conference Record of Thirty-Second Asilomar Conference on Signals Systems and Computers, vol. 1, pp. 99-103, 1998.


Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.