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Image and video coding using a wavelet decomposition
SIGNAL
PROCESSING ELSEVIER
Signal Processing39 (1994) 347
Thesis alert
Herjan J. Barnard*
Image and video coding using a wavelet decomposition The thesis starts with a derivation of the wavelet theory. A consistent notation and naming for the wavelet theory is presented analogous to the Fourier theory, depending on the signal being discrete or continuous, and finite or infinite length. The differences and similarities between the formulas are shown in a table. The discrete wavelet transform (DWT) is shown to be equal to a repeated subband decomposition with a two-channel filter bank. Several diagrams illustrate how the signal extension at the boundaries of finite length signals should be performed to preserve the perfect reconstruction property. Further, a method is introduced to decompose arbitrary length signals into subbands without producing extra subband samples. Next, the application of the DWT to image and video coding is considered. The objective and subjective coding performances of the DWT are compared for various filters originating from both the subband coding theory and the wavelet theory. In general, no large differences in coding performance appear, but the biorthogonal linear phase wavelet filters perform best, followed by almost all linear phase subband coding filters, and the non-linear phase wavelet filters. The regularity of a filter seems only to be important for the synthesis filters, and a regularity order of 2 seems to be sufficient. Several tables and figures with the characteristics of all filters under consideration are shown in the
appendix. In addition, improvements of some wellknown Johnston filters are suggested. In the third place, the quincunx 2-D DWT is considered. It is expected to perform better than the dyadic 2-D DWT for some classes of images, like aerial photographs and images with many diagonal structures, but in the experiments the quincunx 2-D DWT shows a lower performance than the dyadic 2-D DWT, both in terms of objective and subjective measures. Finally, a region-based discrete wavelet transform (RBDWT) is introduced to code the texture in a region-based image coding scheme. This RBDWT has the advantage that it enables to distribute the available bit rate over subbands as well as regions. It differs from other texture coding methods like polynomial fitting, that the regions should be rather large, while the RBDWT takes care of the remaining edges inside the regions. Further, the computational complexity is very low. The implementation is explained in detail, and an image coding scheme is presented. The coding performance of the RBDWT is compared to the performance of the standard DWT. The signal-to-noise ratio is slightly lower, but in terms of subjective visual quality the new method tends to be better, because of the smaller ringing artefacts and the better preservation of edges. Therefore, the new RBDWT image coding technique is at least competitive to the standard DWT. Several suggestions for further research in this new direction are given.
*Thesis advisors:Prof.Jan Biemondand Dr. Jos H. Weber.InformationTheoryGroup, Departmentof ElectricalEngineering,Delft Universityof Technology,P.O. Box 5031,2600GA Delft,The Netherlands.E-mailcorrespondenceto [email protected]. Elsevier ScienceB.V.
PROCESSING ELSEVIER
Signal Processing39 (1994) 347
Thesis alert
Herjan J. Barnard*
Image and video coding using a wavelet decomposition The thesis starts with a derivation of the wavelet theory. A consistent notation and naming for the wavelet theory is presented analogous to the Fourier theory, depending on the signal being discrete or continuous, and finite or infinite length. The differences and similarities between the formulas are shown in a table. The discrete wavelet transform (DWT) is shown to be equal to a repeated subband decomposition with a two-channel filter bank. Several diagrams illustrate how the signal extension at the boundaries of finite length signals should be performed to preserve the perfect reconstruction property. Further, a method is introduced to decompose arbitrary length signals into subbands without producing extra subband samples. Next, the application of the DWT to image and video coding is considered. The objective and subjective coding performances of the DWT are compared for various filters originating from both the subband coding theory and the wavelet theory. In general, no large differences in coding performance appear, but the biorthogonal linear phase wavelet filters perform best, followed by almost all linear phase subband coding filters, and the non-linear phase wavelet filters. The regularity of a filter seems only to be important for the synthesis filters, and a regularity order of 2 seems to be sufficient. Several tables and figures with the characteristics of all filters under consideration are shown in the
appendix. In addition, improvements of some wellknown Johnston filters are suggested. In the third place, the quincunx 2-D DWT is considered. It is expected to perform better than the dyadic 2-D DWT for some classes of images, like aerial photographs and images with many diagonal structures, but in the experiments the quincunx 2-D DWT shows a lower performance than the dyadic 2-D DWT, both in terms of objective and subjective measures. Finally, a region-based discrete wavelet transform (RBDWT) is introduced to code the texture in a region-based image coding scheme. This RBDWT has the advantage that it enables to distribute the available bit rate over subbands as well as regions. It differs from other texture coding methods like polynomial fitting, that the regions should be rather large, while the RBDWT takes care of the remaining edges inside the regions. Further, the computational complexity is very low. The implementation is explained in detail, and an image coding scheme is presented. The coding performance of the RBDWT is compared to the performance of the standard DWT. The signal-to-noise ratio is slightly lower, but in terms of subjective visual quality the new method tends to be better, because of the smaller ringing artefacts and the better preservation of edges. Therefore, the new RBDWT image coding technique is at least competitive to the standard DWT. Several suggestions for further research in this new direction are given.
*Thesis advisors:Prof.Jan Biemondand Dr. Jos H. Weber.InformationTheoryGroup, Departmentof ElectricalEngineering,Delft Universityof Technology,P.O. Box 5031,2600GA Delft,The Netherlands.E-mailcorrespondenceto [email protected]. Elsevier ScienceB.V.