Optimal Linear Processing for Image and Video Coding
Onur G. Guleryuz · 1997
Linear methods form the basis of current high-performance image and video coders. In image coding, energy-compacting linear transforms are utilized to decorrelate and sparsify the source. In the coding of video sequences, a simple linear predictive loop is used to reduce the important temporal dependencies. This dissertation presents a body of work concerned with the analysis and optimization of the linear processing employed in the compression of still images and video sequences. The transform coding of images is analyzed from a common standpoint in order to generate a framework for the design of optimal transforms. Using a general energy-com-paction measure, the relationship between optimal transforms and optimal linear estima-tors is determined, resulting in energy-compaction-optimized nonorthogonal transforms. On the class of signals exhibiting localized discontinuities (edges), it is shown that the global statistics of the class are corrupted by the presence of edges and do not reflect the possibly strong local dependencies. Using a statistical model, we show that coding-efficient transforms for this class must be localized. In particular, we establish the rate-distortion performance of wavelet representations on this class.