Hidden Markov Tree Models for Complex Wavelet Transforms

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Title: Hidden Markov Tree Models for Complex Wavelet Transforms
Author: Romberg, Justin; Choi, Hyeokho; Baraniuk, Richard G.; Kingsbury, Nicholas G.
Type: Journal Paper
Keywords: complex wavelets; hidden markov models; image denoising
Citation: J. Romberg, H. Choi, R. G. Baraniuk and N. G. Kingsbury, "Hidden Markov Tree Models for Complex Wavelet Transforms," IEEE Transactions on Signal Processing, 2002.
Abstract: 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.
Date Published: 2002-05-01

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  • ECE Publications [1030 items]
    Publications by Rice University Electrical and Computer Engineering faculty and graduate students
  • DSP Publications [508 items]
    Publications by Rice Faculty and graduate students in digital signal processing.