A new stabilized zero — Crossing representation in the wavelet transform domain and its application to image processing

We present a new stabilized zero-crossing representation with a salient feature that the signal reconstruction problem reduces to a typical minimum-norm optimization problem, the solution of which is formulated as a linear simultaneous equation, and develop an iterative algorithm for signal reconstruction. Moreover, we extend them to the two-dimensional case. Furthermore, we introduce a threshold operation based on edge intensity to reduce the amount of information in the stabilized zero-crossing representation, and experimentally demonstrate that the threshold operation works well.