IMAGE-RECONSTRUCTION BASED ON ZERO-CROSSING REPRESENTATIONS OF WAVELET TRANSFORM

This paper discusses a reconstruction method of the image signal from the zero-crossing representation. First, the one- and two-dimensional multiscale wavelet transforms are described which have the completenes s and the translation invariance. A new zero-crossing representation i s proposed in which the zero-crossing points are extracted from the mu ltiscale wavelet transform. The information concerning the maximum val ue (the minimum value when negative) between two consecutive zero-cros sing points as well as its position is combined. Then it is shown that the original signal can be reconstructed with a stable and fast conve rgence from the zero-crossing representation of the signal through the iterated projections to the convex set. The effect of the wavelet bas is filter on the convergence in the reconstruction is investigated, an d a necessary condition for the optimal basis filter is derived consid ering the convergence. Finally, a new basis filter is designed using t he B-spline function and the usefulness of the proposed method is demo nstrated for the one-dimensional signal and the image signal. It is sh own also that the signal reconstruction procedure converges with stabi lity, even if there exists an error at the extracted zero-crossing poi nt.