Complex Wavelet-Based Compression

This thesis gives an introduction to the discrete complex wavelet transform, followed by a mean square error based performance analysis of complex wavelet-based compression of synthetic aperture radar (SAR) data within the software framework of the JPEG 2000 Verification Model (VM). With the many varied wavelets available to the signal processing community, it can be difficult to determine which wavelet is optimally suited for a particular type of signal. Often the easiest method to determine suitability is to simply test them. This thesis compares the 9/7 Daubechies wavelet with the complex-valued symmetric Daubechies wavelets for the task of lossy compression of SAR data. This work has shown that symmetric Daubechies wavelets (SDW) can achieve better compression then the 9/7 Daubechies wavelet for SAR data when using MSE as the benchmark. The SDW are also shown to have less prounounced phase artifacts. These results have all been achieved despite the fact that the lossy compression methods in the JPEG 2000 VM were not designed with complex-valued wavelets in mind. Any future codec work will be able to exploit the newly available phase information for additional gains without having to start from a position of disadvantage.