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The paper discusses the theory behind the dual-tree transform, shows how complex wavelets with good properties can be designed, and illustrates a range of applications in signal and image processing. The authors use the complex number symbol C in CWT to avoid confusion with the often-used acronym CWT for the (different) continuous wavelet transform. The… (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 its… (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 performance of various estimators, such as maximum a posteriori (MAP) is strongly dependent on correctness of the proposed model for noise-free data distribution. Therefore, the selection of a proper model for distribution of wavelet coefficients is important in the wavelet based image denoising. This paper presents a new image denoising algorithm based… (More)

The two-band discrete wavelet transform (DWT) provides an octave-band analysis in the frequency domain, but this might not be ldquooptimalrdquo 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… (More)

This paper uses probability models on expansive wavelet transform coefficients with interpolation constraints to estimate missing blocks in images. We use simple probability models on wavelet coefficients to formulate the estimation process as a linear programming problem and solve it to recover the missing pixels. Our formulation is general and can be… (More)

We propose a non-linear mapping function for digital image enhancement in the wavelet domain, which amplifies mid-range coefficients more than small and large coefficients. We derive this function based on a statistical model of the wavelet coefficients. This three-component mixture model describes the coefficients in each subband as a mixture of small,… (More)

This paper describes several types of matching exercises for introductory digital signal processing. The paper presents example exercises in four areas of DSP: the discrete Fourier transform, weighted least square FIR filter design, minimum-phase FIR filters, and the short-time Fourier transform. These exercises tests for conceptual understanding of… (More)

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