Multi-dimensional wavelet coding- algorithms and implementations

During the last decade, wavelet technology has been integrated into a plethora of applications. Especially in the image compression community it was received with a lot of enthusiasm. Hence, it has been accepted as an enabling technology in several standards treating multimedia content, i.e. the ISO/IEC standards JPEG2000 and MPEG-4. This dissertation covers aspects of wavelet image coding, which are not well covered yet. Additionally, it tries to break down paradigms that have prevented for a long-time − and sometimes still are preventing − the breakthrough of wavelet-based coding technology in specific application domains.A first theme is volumetric image coding. Few proposals have been made to exploit wavelet technology for this type of data, and most of them are based on embedded zero-tree coding principles. We propose new volumetric coding schemes exploiting quad-tree splitting and layered zero coding, algorithms that are well known for their two-dimensional counterparts. Moreover, also a new 3D DCT based encoder is introduced as reference for DCT-based coding schemes. An elaborate evaluation is made of these coders, including a comparison with coding techniques such as JPEG2000 (with and without a 3D wavelet transform), 3D SPIHT and 3D SB-SPECK. The aforementioned techniques are profiled for their lossless as well as their lossy coding behaviour. It is studied whether compression of volumetric medical data really benefits from the fact that volumetric wavelet-based coders are capable of exploiting possible correlations in the third dimension. The influence of the transform, the quantization and the entropy coding modules on this behaviour is assessed. Additionally, a set of lossless integer filter kernels was evaluated.Typically, the performance of image coders is evaluated based on objective criteria (e.g. PSNR). Hence, most wavelet coders are constructed such that they deliver an optimal rate-distortion performance. Unfortunately, the rate-distortion performance does not reflect correctly the perceived image quality after decoding. Therefore, mechanisms have to be incorporated in the coding/decoding engines that take into account properties of the human visual system, in order to adequately support an optimal perceived quality at each bit-rate. An overview is given of the principles to be exploited during encoding (visual frequency weighing, visual masking, pre- and post-processing techniques), and how the encoders/decoders can be altered to enable efficient support for this functionality.Region-of-interest coding is another interesting feature to improve the efficiency with which large datasets can be consulted over systems with limited transmission/memory bandwidth. The different approaches to equip coders with this functionality are discussed, as well as the protocols that should be followed by the application.A final section of this dissertation tackles one of the main bottlenecks that was, and partially still is, preventing wavelet coding techniques from breaking through in the marketplace: its (assumed) complexity. It is demonstrated that by carefully tuning the algorithms – applying a particular data transfer and storage (DTS) optimisation methodology – the implementation cost of this type of encoders can be reduced significantly. As a case study the embedded zero-tree coder is examined and optimised, focusing both on the wavelet transform part and the zero-tree coding module. For the wavelet transform module different lifting-scheme targeted instantiations are theoretically studied: the row-column approach, the (multiplexed) line-based version, the recursive pyramid algorithm and finally the local