Hidden Markov Tree Models for Complex Wavelet Transforms

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dc.citation.bibtexNamearticleen_US
dc.citation.journalTitleIEEE Transactions on Signal Processingen_US
dc.contributor.authorRomberg, Justinen_US
dc.contributor.authorChoi, Hyeokhoen_US
dc.contributor.authorBaraniuk, Richard G.en_US
dc.contributor.authorKingsbury, Nicholas G.en_US
dc.contributor.orgCenter for Multimedia Communications (http://cmc.rice.edu/)en_US
dc.contributor.orgDigital Signal Processing (http://dsp.rice.edu/)en_US
dc.date.accessioned2007-10-31T01:02:46Zen_US
dc.date.available2007-10-31T01:02:46Zen_US
dc.date.issued2002-05-01en_US
dc.date.modified2006-06-26en_US
dc.date.submitted2002-07-10en_US
dc.descriptionJournal Paperen_US
dc.description.abstractMultiresolution 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.en_US
dc.identifier.citationJ. Romberg, H. Choi, R. G. Baraniuk and N. G. Kingsbury, "Hidden Markov Tree Models for Complex Wavelet Transforms," <i>IEEE Transactions on Signal Processing,</i> 2002.en_US
dc.identifier.urihttps://hdl.handle.net/1911/20299en_US
dc.language.isoengen_US
dc.subjectcomplex waveletsen_US
dc.subjecthidden markov modelsen_US
dc.subjectimage denoisingen_US
dc.subject.keywordcomplex waveletsen_US
dc.subject.keywordhidden markov modelsen_US
dc.subject.keywordimage denoisingen_US
dc.subject.otherImage Processing and Pattern analysisen_US
dc.subject.otherWavelet based Signal/Image Processingen_US
dc.titleHidden Markov Tree Models for Complex Wavelet Transformsen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
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