Browsing by Author "Kingsbury, Nicholas G."

Now showing 1 - 4 of 4
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    The Dual-Tree Complex Wavelet Transform
    (2005-11-01) Selesnick, Ivan W.; Baraniuk, Richard G.; Kingsbury, Nicholas G.; Digital Signal Processing (http://dsp.rice.edu/)
    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 four fundamentals, intertwined shortcomings of wavelet transform and some solutions are also discussed. Several methods for filter design are described for dual-tree CWT that demonstrates with relatively short filters, an effective invertible approximately analytic wavelet transform can indeed be implemented using the dual-tree approach.
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    Hidden Markov Tree Modeling of Complex Wavelet Transforms
    (2000-06-01) Choi, Hyeokho; Romberg, Justin; Baraniuk, Richard G.; Kingsbury, Nicholas G.; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/)
    Multiresolution signal and image models such as the hidden Markov tree aim to capture the statistical structure of smooth and singular (edgy) regions. Unfortunately, models based on the orthogonal wavelet transform suffer from shift-variance, making them less accurate and realistic. In this paper, we extend the HMT modeling framework to the complex wavelet transform, which features near shift-invariance and improved angular resolution compared to the standard wavelet transform. The model is computationally efficient (with linear-time computation and processing algorithms) and applicable to general Bayesian inference problems as a prior density for the data. In a simple estimation experiment, the complex wavelet HMT model outperforms a number of high-performance denoising algorithms, including redundant wavelet thresholding (cycle spinning) and the redundant HMT.
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    Hidden Markov Tree Models for Complex Wavelet Transforms
    (2002-05-01) Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G.; Kingsbury, Nicholas G.; Center for Multimedia Communications (http://cmc.rice.edu/); Digital Signal Processing (http://dsp.rice.edu/)
    Multiresolution models such as the hidden Markov tree (HMT) aim to capture the statistical structure of signals and images by leveraging two key wavelet transform properties: wavelet coefficients representing smooth/singular regions in a signal have small/large magnitude, and small/large magnitudes persist through scale. Unfortunately, the HMT based on the conventional (fully decimated) wavelet transform suffers from shift-variance, making it less accurate and realistic. In this paper, we extend the HMT modeling framework to the complex wavelet transform, which features near shift-invariance and improved directionality compared to the standard wavelet transform. The complex HMT model is computationally efficient (with linear-time computation and processing algorithms) and applicable to general Bayesian inference problems as a prior density for images. We demonstrate the effectiveness of the model with two applications. In a simple estimation experiment, the complex wavelet HMT model outperforms a number of high-performance denoising algorithms, including redundant wavelet thresholding (cycle spinning) and the redundant HMT. A multiscale maximum likelihood texture classification algorithm produces fewer errors with the new model than with a standard HMT.
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    Multiscale Classification using Complex Wavelets and Hidden Markov Tree Models
    (2000-09-01) Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G.; Kingsbury, Nicholas G.; Digital Signal Processing (http://dsp.rice.edu/)
    Multiresolution signal and image models such as the hidden Markov tree (HMT) aim to capture the statistical structure of smooth and singular (textured and edgy) regions. Unfortunately, models based on the orthogonalwavelet transform suffer from shift-variance, making them less accurate and realistic. In this paper, we extend the HMT modeling framework to the complex wavelet transform, which features near shift-invariance and improved angular resolution compared to the standard wavelet transform. The model is computationally efficient (featuring linear-time computation and processing algorithms) and applicable to general Bayesian inference problems as a prior density for the data. In this paper, we develop a simple multiscale maximum likelihood classification scheme based on the complex wavelet HMT that outperforms those based on traditional real-valued wavelet transforms. The resulting classification can be used as a front end in a more sophisticated multiscale segmentation algorithm.