Image reconstruction based on zero‐crossing representations of wavelet transform
Cha Keon Cheong, Kiyoha Aizawa, Mitsutoshi Hatori, Takahiro Saito · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1995
Abstract 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 completeness and the translation invariance. A new zero‐crossing representation is proposed in which the zero‐crossing points are extracted from the multiscale wavelet transform. the information concerning the maximum value (the minimum value when negative) between two consecutive zero‐crossing points as well as its position is combined. Then it is shown that the original signal can be reconstructed with a stable and fast convergence from the zero‐crossing representation of the signal through the iterated projections to the convex set. The effect of the wavelet basis filter on the convergence in the reconstruction is investigated, and a necessary condition for the optimal basis filter is derived considering the convergence. Finally, a new basis filter is designed using the B‐spline function and the usefulness of the proposed method is demonstrated for the one‐dimensional signal and the image signal. It is shown also that the signal reconstruction procedure converges with stability, even if there exists an error at the extracted zero‐crossing point.