Orthogonal vs. Biorthogonal Wavelets for Image Compression

Effective image compression requires a non-expansive discrete wavelet transform (DWT) be employed; consequently, image border extension is a critical issue. Ideally, the image border extension method should not introduce distortion under compression. It has been shown in literature that symmetric extension performs better than periodic extension. However, the non-expansive, symmetric extension using fast Fourier transform and circular convolution DWT methods require symmetric filters. This precludes orthogonal wavelets for image compression since they cannot simultaneously possess the desirable properties of orthogonality and symmetry. Thus, biorthogonal wavelets have been the de facto standard for image compression applications. The viability of symmetric extension with biorthogonal wavelets is the primary reason cited for their superior performance. Recent matrix-based techniques for computing a non-expansive DWT have suggested the possibility of implementing symmetric extension with orthogonal wavelets. For the first time, this thesis analyzes and compares orthogonal and biorthogonal wavelets with symmetric extension. Our results indicate a significant performance improvement for orthogonal wavelets when they employ symmetric extension. Furthermore, our analysis also identifies that linear (or near-linear) phase filters are critical to compression performance—an issue that has not been recognized to date. We also demonstrate that biorthogonal and orthogonal wavelets generate similar compression performance when they have similar filter properties and both employ symmetric extension. The biorthogonal wavelets indicate a slight performance advantage for low frequency images ; however, this advantage is significantly smaller than recently published results and is explained in terms of wavelet properties not previously considered. Acknowledgments I express my sincere gratitude to my advisor Dr. Amy Bell for her technical and financial support which made this thesis possible. Her constant encouragement, suggestions and ideas have been invaluable to this work. I immensely appreciate the time she devoted reviewing my writing and vastly improving my technical writing skills. Her thoroughness, discipline and work ethic are laudable and worthy of emulation. I would like to thank Dr. Brian Woerner and Dr. Lynn Abbott for reviewing my work and agreeing to serve on my committee. I am also grateful to Dr. Karen Duca in VBI for her financial support and the opportunity to work on some interesting biomedical signal processing problems. I am thankful to my fellow DSPCL colleagues Kishore Kotteri and Krishnaraj Varma for their technical help and insightful suggestions that went a long way in shaping this thesis. My interactions with them greatly improved my technical knowledge and research skills. I am also …