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[ A coherent framework for multiscale signal and image processing ] T he dual-tree complex wavelet transform (CWT) is a relatively recent enhancement to the discrete wavelet transform (DWT), with important additional properties: It is nearly shift invariant and directionally selective in two and higher dimensions. It achieves this with a redundancy factor… (More)

—Several authors have demonstrated that significant improvements can be obtained in wavelet-based signal processing by utilizing a pair of wavelet transforms where the wavelets form a Hilbert transform pair. This paper describes design procedures, based on spectral factorization, for the design of pairs of dyadic wavelet bases where the two wavelets form an… (More)

—Most simple nonlinear thresholding rules for wavelet-based denoising assume that the wavelet coefficients are independent. However, wavelet coefficients of natural images have significant dependencies. In this paper, we will only consider the dependencies between the coefficients and their parents in detail. For this purpose, new non-Gaussian bivariate… (More)

—This paper describes a discrete-time wavelet transform for which the Q-factor is easily specified. Hence, the transform can be tuned according to the oscillatory behavior of the signal to which it is applied. The transform is based on a real-valued scaling factor (dilation-factor) and is implemented using a perfect reconstruction over-sampled filter bank… (More)

This paper introduces a novel speckle reduction method based on thresholding the wavelet coeecients of the logarithmically transformed image. The method is computational eecient and can signiicantly reduce the speckle while preserving the resolution of the original image. Both soft and hard thresholding schemes are studied and the results are compared. When… (More)

—This paper highlights the differences between traditional wavelet and multiwavelet bases with equal approximation order. Because multiwavelet bases normally lack important properties that traditional wavelet bases (of equal approximation order) possess, the associated discrete multiwavelet transform is less useful for signal processing unless it is… (More)

This paper explores the use of a recently introduced 3-D dual-tree discrete wavelet transform (DDWT) for video coding. The 3-D DDWT is an attractive video representation because it siolates motion along different directions in separate subbands. However, it is an overcomplete transform with 8:1 or 4:1 redundancy. Based on the effectiveness of the iterative… (More)

The 2-band discrete wavelet transform (DWT) provides an octave-band analysis in the frequency domain, but this might not be 'optimal' for a given signal. The discrete wavelet packet transform (DWPT) provides a dictionary of bases over which one can search for an optimal representation (without constraining the analysis to an octave-band one) for the signal… (More)

- Ivan W Selesnick, Richard G Baraniuk, Nick Kingsbury
- 2005

The dual-tree complex wavelet transform (CWT) is a relatively recent enhancement of the discrete wavelet transform (DWT) with important additional properties: It is nearly shift-invariant and directionally selective in two and higher dimensions. It achieves this with a redundancy factor of only 2 d for d-dimensional signals, which is substantially lower… (More)

—This paper introduces the double-density dual-tree discrete wavelet transform (DWT), which is a DWT that combines the double-density DWT and the dual-tree DWT, each of which has its own characteristics and advantages. The transform corresponds to a new family of dyadic wavelet tight frames based on two scaling functions and four distinct wavelets. One pair… (More)