Title page for ETD etd-09172003-111540

Type of Document Master's Thesis
Author Rout, Satyabrata
Author's Email Address srout@vt.edu
URN etd-09172003-111540
Title Orthogonal vs. Biorthogonal Wavelets for Image Compression
Degree Master of Science
Department Electrical and Computer Engineering
Advisory Committee
Advisor Name Title
Bell, Amy E. Committee Chair
Abbott, A. Lynn Committee Member
Woerner, Brain D. Committee Member
  • periodic extension
  • DWT implementation
  • biorthogonal wavelet
  • orthogonal wavelet
  • symmetric extension
Date of Defense 2003-08-21
Availability unrestricted
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.

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