No abstract

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, threeband 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.

Poor directional selectivity, a major disadvantage of the 2D separable discrete wavelet transform DWT, has heretofore been circumvented either by using highly redundant, nonseparable wavelet transforms or by using restrictive designs to obtain a pair of wavelet trees. In this paper, we demonstrate that superior directional selectivity may be obtained with no redundancy in any separable wavelet transform. We achieve this by projecting the wavelet transform coe cients onto the Softy space of signals and decimating before processing. A novel reconstruction step guarantees perfect reconstruction within this critically-sampled framework.

No abstract

Wavelet-domain hidden Markov models (HMMs) are powerful tools for modeling the statistical properties of wavelet transforms. By characterizing the joint statistics of wavelet coe cients, HMMs e ciently capture the characteristics of many real-world signals. When applied to images, the model can characterize the joint statistics between pixels, providing a very good classi er for textures. Utilizing the inherent tree structure of waveletdomain HMMs, classi cation of textures at various scales is possible, furnishing a natural tool for multiscale texture segmentation. In this paper, we introduce a new multiscale texture segmentation algorithm based on wavelet-domain hidden Markov trees (HMTs). We apply this new technique to the segmentation of dip-cube time slices.