Wavelet Based Color Image Compression and Mathematical Analysis of Sign Entropy Coding
One of the advantages of the Discrete Wavelet Transform (DWT) compared to Fourier Transform (e.g. Discrete Cosine Transform DCT) is its ability to provide both spatial and frequency localization of image energy. However, WT coefficients, like DCT coefficients, are defined by magnitude as well as sign. While algorithms exist for the coding of wavelet coefficients magnitude, there are no efficient for coding their sign. In this paper, we propose a new method based on separate entropy coding of sign and magnitude of wavelet coefficients. The proposed method is applied to the standard color test images Lena, Peppers, and Mandrill. We have shown that sign information of wavelet coefficients as well for the luminance as for the chrominance, and the refinement information of the quantized wavelet coefficients may not be encoded by an estimated probability of 0.5. The proposed method is evaluated; the results obtained are compared to JPEG2000 and SPIHT codec. We have shown that the proposed method has significantly outperformed the JPEG2000 and SPIHT codec as well in terms of PSNR as in subjective quality. We have proved, by an original mathematical analysis of the entropy, that the proposed method uses a minimum bit allocation in the sign information coding.
Keywords: : Color Image Compression, Wavelet Transform, Entropy Coding, Sign, Magnitude
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ABOUT THE AUTHORS
Mbainaibeye Jérôme
Dr. Mbainaibeye Jérôme received the Master degree in Signal Processing and the PhD degree in Electrical engineering at the National Engineering High School of Tunis (ENIT), Tunisia, in October 1997 and July 2002 respectively. From 2003 to 2008 he has joined the Faculty of Sciences at Universite; 7 Novembre à Carthage, in Tunisia as Assistant Professor in the department of Computer Science. Since September 2008, he has joined the Department of Technogies at the Faculty of Exact & Applied Sciences, University of N’djaména in Chad as Assistant Professor. He has published several papers in international scientific journals and conferences proceedings. He is member of the Systems and Signal Processing Laboratory at ENIT and is an associated researcher in XLIM Signal, Images and Communication Laboratory department, University of Poitiers, France. His research activities include Digital Signal Processing, Image Processing, Image analysis, Image and Video Compression, Wavelet Transform and its applications.
Noureddine Ellouze
Pr. Noureddine Ellouze received a PhD degree in 1977 from l’Institut National Polytechnique at Paul Sabatier University (Toulouse, France), and Electronic Engineer Diploma from ENSEEIHT in 1968 at the same university. He have served as Director of Electrical Department at ENIT from 1978 to 1983, General Manager and President of the Research Institute on Informatics and Telecommunications (IRSIT) from 1987 to 1990, President of the same Institute from 1990 to 1994. He is now Director of Signal Processing Research Laboratory (LSTS) at ENIT and is in charge of Control and Signal Processing Master degree at ENIT. Pr Ellouze is IEEE fellow since 1987, he directed multiple Master thesis and PhD thesis and published over 200 scientific papers in journals and conference proceedings. He is chief editor of the scientific journal Annales Maghrébines de l’Ingénieur. His research interests include Neural Networks and Fuzzy Classification, Pattern Recognition, Signal Processing and Image Processing applied in biomedical, Multimedia, and Man Machine Communication.
Christian Olivier
Pr. Christian Olivier received the degree in Mathematics (Signal Processing) in 1979. His major interest was in stochastic process modelling. He was an Associate Professor at the University of Rouen in France from 1987 to 1997, where his research area was mathematical tools for image segmentation, pattern analysis and recognition. Then he joined the University of Poitiers as a Professor. His research is always mathematical tools but for information representation and measurement, specially for image, video coding and wireless transmission in a joint coding strategy.
Mbainaibeye Jérôme
Dr. Mbainaibeye Jérôme received the Master degree in Signal Processing and the PhD degree in Electrical engineering at the National Engineering High School of Tunis (ENIT), Tunisia, in October 1997 and July 2002 respectively. From 2003 to 2008 he has joined the Faculty of Sciences at Universite; 7 Novembre à Carthage, in Tunisia as Assistant Professor in the department of Computer Science. Since September 2008, he has joined the Department of Technogies at the Faculty of Exact & Applied Sciences, University of N’djaména in Chad as Assistant Professor. He has published several papers in international scientific journals and conferences proceedings. He is member of the Systems and Signal Processing Laboratory at ENIT and is an associated researcher in XLIM Signal, Images and Communication Laboratory department, University of Poitiers, France. His research activities include Digital Signal Processing, Image Processing, Image analysis, Image and Video Compression, Wavelet Transform and its applications.
Noureddine Ellouze
Pr. Noureddine Ellouze received a PhD degree in 1977 from l’Institut National Polytechnique at Paul Sabatier University (Toulouse, France), and Electronic Engineer Diploma from ENSEEIHT in 1968 at the same university. He have served as Director of Electrical Department at ENIT from 1978 to 1983, General Manager and President of the Research Institute on Informatics and Telecommunications (IRSIT) from 1987 to 1990, President of the same Institute from 1990 to 1994. He is now Director of Signal Processing Research Laboratory (LSTS) at ENIT and is in charge of Control and Signal Processing Master degree at ENIT. Pr Ellouze is IEEE fellow since 1987, he directed multiple Master thesis and PhD thesis and published over 200 scientific papers in journals and conference proceedings. He is chief editor of the scientific journal Annales Maghrébines de l’Ingénieur. His research interests include Neural Networks and Fuzzy Classification, Pattern Recognition, Signal Processing and Image Processing applied in biomedical, Multimedia, and Man Machine Communication.
Christian Olivier
Pr. Christian Olivier received the degree in Mathematics (Signal Processing) in 1979. His major interest was in stochastic process modelling. He was an Associate Professor at the University of Rouen in France from 1987 to 1997, where his research area was mathematical tools for image segmentation, pattern analysis and recognition. Then he joined the University of Poitiers as a Professor. His research is always mathematical tools but for information representation and measurement, specially for image, video coding and wireless transmission in a joint coding strategy.
