Browsing by Author "van Spaendonck, Rutger"

Now showing 1 - 6 of 6
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    Complex Wavelet Transforms with Allpass Filters
    (2003-08-20) Fernandes, Felix; Selesnick, Ivan W.; van Spaendonck, Rutger; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)
    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 the results when different allpass systems are used. In the earlier work, maximally flat delay allpass systems were used. In this paper, it is shown that an allpass system designed according to the minimax criterion yields improvements for the complex discrete wavelet transforms.
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    Directional Complex-Wavelet Processing
    (2000-08-20) Fernandes, Felix; van Spaendonck, Rutger; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)
    Poor directional selectivity, a major disadvantage of the separable 2D discrete wavelet transform (DWT), has previously 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 no redundancy in any separable wavelet transform. We achieve this by projecting the wavelet coefficients to separate approximately the positive and negative frequencies. Subsequent decimation maintains non-redundancy. A novel reconstruction step guarantees perfect reconstruction within this critically-sampled framework. Although our transform generates complex-valued coefficients, it may be implemented with a fast algorithm that uses only real arithmetic. We also explain how redundancy may be judiciously introduced into our transform to benefit certain applications. To demonstrate the efficacy of our projection technique, we show that it achieves state-of-the-art performance in a seismic image-processing application.
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    Directional Scale Analysis for Seismic Interpretation
    (1999-11-01) van Spaendonck, Rutger; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
    A combined space-Fourier representation focused on directional scale analysis is presented. The method leads to a space-log polar frequency distribution. Application to seismic data shows differentiation in scale and orientation. Attributes are extracted to illustrate this differentiation.
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    Multiscale Texture Segmentation of Dip-cube Slices using Wavelet-domain Hidden Markov Trees
    (1999-11-01) Magrin-Chagnolleau, Ivan; Choi, Hyeokho; van Spaendonck, Rutger; Steeghs, Philippe; Baraniuk, Richard G.; Digital Signal Processing (http://dsp.rice.edu/)
    Wavelet-domain Hidden Markov Models (HMMs) are powerful tools for modeling the statistical properties of wavelet coefficients. By characterizing the joint statistics of wavelet coefficients, HMMs efficiently capture the characteristics of many real-world signals. When applied to images, the model can characterize the joint statistics between pixels, providing a very good classifier for textures. Utilizing the inherent tree structure of wavelet-domain HMM, classification of textures at various scales is possible, furnishing a natural tool for multiscale texture segmentation. In this paper, we introduce a new multiscale texture segmentation algorithm based on wavelet-domain HMM. Based on the multiscale classification results obtained from the wavelet-domain HMM, we develop a method to combine the multiscale classification results to generate a reliable segmentation of the texture images. We apply this new technique to the segmentation of dip-cube slices.
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    A New Framework for Complex Wavelet Transforms
    (2003-06-20) Fernandes, Felix; van Spaendonck, Rutger; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)
    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 two-stage mapping-based complex wavelet transforms that consist of a mapping onto a complex function space followed by a DWT of the complex mapping. Unlike other popular transforms that also mitigate DWT shortcomings, the decoupled implementation of our transforms has two important advantages. First, the controllable redundancy of the mapping stage offers a balance between degree of shift sensitivity and transform redundancy. This allows us to create a directional, non-redundant, complex wavelet transform with potential benefits for image coding systems. To the best of our knowledge, no other complex wavelet transform is simultaneously directional and non-redundant. The second advantage of our approach is the flexibility to use any DWT in the transform implementation. As an example, we can exploit this flexibility to create the Complex Double-density DWT (CDDWT): a shift-insensitive, directional, complex wavelet transform with a low redundancy of (3m - 1)/(2m - 1) in m dimensions. To the best of our knowledge, no other transform achieves all these properties at a lower redundancy.
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    Orthogonal Hilbert Transform Filter Banks and Wavelets
    (2003-04-01) van Spaendonck, Rutger; Blu, Thierry; Baraniuk, Richard G.; Vetterli, Martin; Digital Signal Processing (http://dsp.rice.edu/)
    Complex wavelet transforms offer the opportunity to perform directional and coherent processing based on the local magnitude and phase of signals and images. Although denoising, segmentation, and image enhancement are significantly improved using complex wavelets, the redundancy of most current transforms hinders their application in compression and related problems. In this paper we introduce a new orthonormal complex wavelet transform with no redundancy for both real- and complex-valued signals. The transform's filter bank features a real low pass filter and two complex high pass filters arranged in a critically sampled three-band structure. Placing symmetry and orthogonality constraints on these filters, we find that each high-pass filter can be factored into a real high pass filter followed by an approximate Hilbert transform filter.