Zero-crossing representation in the wavelet transform domain and signal reconstruction.

The wavelet transform is a practical method for multiresolution analysis. Previously, methods for describing the transformed signal using zero-crossing information and additional complementing information (zero-crossing representation) have been studied. The zero-crossing representation, however, presents problems in that the physical interpretation of the applied additional information is not clear, and reconstruction of the original signal from the zero-crossing representation involves 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 information with clear physical interpretation and has a form that is easy 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 convergence and has lower computional complexity than the conventional method. The proposed zero-crossing representation is extended to the two-dimensional case and is applied to an actual image. It is experimentally 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 degradation of the reconstructed image is examined. © 1998 Scripta Technica, Electron Comm Jpn Pt 3, 82(1): 68–78, 1999 [ABSTRACT FROM AUTHOR]