Orthogonal Hilbert transform filter banks and wavelets

Complex wavelet transforms offer the opportunity to perform directional and coherent processing based on the local magnitude and phase of signals and images. Although denoising, segmentation, and image enhancement are significantly improved using complex wavelets, the redundancy of most current transforms hinders their application in compression and related problems. In this paper we introduce a new orthonormal complex wavelet transform with no redundancy for both real- and complex-valued signals. The transform's filterbank features a real lowpass filter and two complex highpass filters arranged in a critically sampled, three-band structure. Placing symmetry and orthogonality constraints on these filters, we find that each high-pass filter can be factored into a real highpass filter followed by an approximate Hilbert transform filter.