An improved version of the inverse Hyperanalytic Wavelet Transform

The success of wavelet techniques in many fields of signal and image processing was proved to be highly influenced by the properties of the wavelet transform used, mainly the shift-invariance and the directional selectivity. In the present paper we propose an improved version of the inverse hyperanalytic wavelet transform (HWT), which uses hyperanalytic mother wavelets. We have already proposed implementations of the HWT and of its inverse (IHWT). The implementation supposes the computation of the discrete wavelet transform (DWT) of the hyperanalytic signal associated to the input signal. Our old computation method of the IHWT extracts the real part of the signal at the output of the inverse discrete wavelet transform (IDWT). The aim of this paper is a new implementation of the IHWT, which permits a better shift invariance. We will compare this implementation with our previous one, with the DWT and with Kingsbury's double-tree complex wavelet transform (DT CWT).