ZERO-CROSSING REPRESENTATION IN THE WAVELET TRANSFORM DOMAIN AND SIGNAL RECONSTRUCTION

The wavelet transform is a practical method for multiresolution analys is. Previously, methods for describing the transformed signal using ze ro-crossing information and additional complementing information (zero -crossing representation) have been studied. The zero-crossing represe ntation, however, presents problems in that the physical interpretatio n of the applied additional information is not clear, and reconstructi on of the original signal from the zero-crossing representation involv es iterations of nonlinear operations. Other problems include the fact that extension to the multidimensional case is difficult and that the computational complexity is considerable. In this paper, the authors propose a new zero-crossing representation that uses the additional in formation with clear physical interpretation and has a form that is ea sy to handle in signal processing. A method is proposed to reconstruct the original signal from the zero-crossing representation. The method uses iterative linear operations with a theoretical guarantee of conv ergence and has lower computational complexity than the conventional m ethod. The proposed zero-crossing representation is extended to the tw o-dimensional case and is applied to an actual image. It is experiment ally verified that the reconstructed image is a good approximation to the original signal. Furthermore, the amount of additional information in the zero-crossing representation is reduced. The quality degradati on of the reconstructed image is examined. (C) 1998 Scripta Technica.