Rutger L. van Spaendonck

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Complex discrete wavelet transforms have significant advantages over real wavelet transforms for certain signal processing problems. Two approaches to the implementation of complex wavelet transforms have been proposed earlier. Both approaches require discrete-time allpass systems having approximately linear-phase and (fractional) delay. This paper compares(More)
Complex wavelet transforms offer the opportunity to perform directional and coherent processing based on the local magnitude and phase of signals and images. Although demising, segmen-tation, and image enhancement are significantly improved using complex wavelets, the redundancy of most current transforms hinders their application in compression and related(More)
Although the discrete wavelet transform (DWT) is a powerful tool for signal and image processing, it has three serious disadvantages: shift sensitivity, poor directionality, and lack of phase information. To overcome these disadvantages, we introduce multidimensional, mapping-based, complex wavelet transforms that consist of a mapping onto a complex(More)
Shift variance and poor directional selectivity, two major disadvantages of the discrete wavelet transform, have previously been circumvented either by using highly redundant, non-separable wavelet transforms or by using restrictive designs to obtain a pair of wavelet trees with a transform-domain redundancy of 4.0 in 2D. In this paper, we demonstrate that(More)
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(More)
Shift variance and poor directional selectivity, two major disadvantages of the discrete wavelet transform, have previously been circumvented either by using highly redundant, non-separable wavelet transforms or by using restrictive designs to obtain a pair of wavelet trees with a transform-domain redundancy of 4.0 in 2D. In this paper, we demonstrate that(More)
Wavelet-domain hidden Markov models (HMMs) are powerful tools for modeling the statistical properties of wavelet transforms. By characterizing the joint statistics of wavelet coeecients, HMMs eeciently capture the characteristics of many real-world signals. When applied to images, the model can characterize the joint statistics between pixels, providing a(More)
Shift sensitivity, poor directional selectivity and lack of phase information are three major disadvantages of the discrete wavelet transform, In earlier research, we demonstrated that projection-based complex wavelet transforms have excellent directional selectivity and explicit phase information, In this paper, we discuss the theory of projection-based(More)
Computational seismic interpretation and visualization, multiresolution analysis and processing of multi-dimensional seismic data, (time-lapse) seismic imaging and attributes, (orthogonal) complex wavelets, Hilbert transform, wavelet deconvolution.
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