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—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)

—The performance of image-denoising algorithms using wavelet transforms can be improved significantly by taking into account the statistical dependencies among wavelet coefficients as demonstrated by several algorithms presented in the literature. In two earlier papers by the authors, a simple bivariate shrinkage rule is described using a coefficient and… (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)

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 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)

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 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)