Iterative image coding with overcomplete complex wavelet transforms
Nick Kingsbury, T.H. Reeves · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2003
Overcomplete transforms, such as the Dual-Tree Complex Wavelet Transform, can offer more flexible signal representations than critically-sampled transforms such as the Discrete Wavelet Transform. However the process of selecting the optimal set of coefficients to code is much more difficult because many different sets of transform coefficients can represent the same decoded image. We show that large numbers of transform coefficients can be set to zero without much reconstruction quality loss by forcing compensatory changes in the remaining coefficients. We develop a system for achieving these coding aims of coefficient elimination and compensation, based on iterative projection of signals between the image domain and transform domain with a non-linear process (e.g.~centre-clipping or quantization) applied in the transform domain. The convergence properties of such non-linear feedback loops are discussed and several types of non-linearity are proposed and analyzed. The compression performance of the overcomplete scheme is compared with that of the standard Discrete Wavelet Transform, both objectively and subjectively, and is found to offer advantages of up to 0.65 dB in PSNR and significant reduction in visibility of some types of coding artifacts.