A new stabilized zero-crossing representation in the wavelet transform domain and signal reconstruction

Stabilized multiscale zero-crossing representations are well adapted for extracting local features such as edges from images. For almost all the variants of the representation presented so far, signal reconstruction from it has been formulated as a non-linear optimization problem, and the algorithms for it are based on the formulation of projections onto convex sets. However, they have common drawbacks: difficulty in extending the algorithms to the two-dimensional case, fractional sampling interval accuracy in the positions of zero-crossings requisite for almost complete signal reconstruction, and a large amount of computational efforts involved in signal reconstruction. To cope with the drawbacks, 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. With the iterative reconstruction algorithm we can almost perfectly reconstruct an original image from the stabilized zero-crossing representation, and after some dozens of iterations the algorithm provides a reconstruction image with subjectively high picture quality.