Construction of Two Types of Wavelets Based on Edge Detector

Two types of wavelets via the mth cardinal B-spline function have been discussed in our paper, corresponding to the extrema detection and zero-crossings detection respectively. Based on Mallat's wavelet transform and reverse transform theory of 1-D and 2-D signals, we derive the general expressions for the spatial and frequency responses of the filter banks in his wavelet decomposition and deconstruction algorithms for above two detection techniques of two detection techniques. Furthermore, we study in detail the properties of two types of wavelets, analyse their roles in the wavelet transform, and compare their differences on the detection of irregular structures of the signal.