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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)
—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)
—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)
—This paper considers the design of pairs of wavelet bases where the wavelets form a Hilbert transform pair. The derivation is based on the limit functions defined by the infinite product formula. It is found that the scaling filters should be offset from one another by a half sample. This gives an alternative derivation and explanation for the result by(More)
The denoising of video data should take into account both temporal and spatial dimensions, however, true 3D transforms are rarely used for video denoising. Separable 3-D transforms have artifacts that degrade their performance in applications. This paper describes the design and application of the non-separable oriented 3-D dual-tree wavelet transform for(More)
Most simple nonlinear thresholding rules for wavelet-based denoising assume the wavelet coefficients are independent. However, wavelet coefficients of natural images have significant dependency. In this paper, a new heavy-tailed bivari-ate pdf is proposed to model the statistics of wavelet coefficients , and a simple nonlinear threshold function (shrinkage(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)
—We investigate a subband adaptive version of the popular iterative shrinkage/thresholding algorithm that takes different update steps and thresholds for each subband. In particular, we provide a condition that ensures convergence and discuss why making the algorithm subband adaptive accelerates the convergence. We also give an algorithm to select(More)
—This paper describes a new class of maximally flat low-pass recursive digital filters. The filters are realizable as a parallel sum of two all-pass filters, a structure for which low-complexity low-noise implementations exist. Note that, with the classical Butterworth filter of degree N which is retrieved as a special case, it is not possible to adjust the(More)