Bayesian tree-structured image modeling using wavelet-domain hidden Markov models
Bayesian tree-structured image modeling using wavelet-domain hidden Markov models
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DOI：
10.1117/12.351328
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发表时间：
1999-06
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影响因子：
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通讯作者：
J. Romberg;Hyeokho Choi;Richard Baraniuk
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文献类型：
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作者：
J. Romberg;Hyeokho Choi;Richard Baraniuk
小波域隐马尔可夫模型已被证明是统计信号和图像处理的有用工具。隐马尔可夫树模型捕捉了真实数据的小波系数联合密度的关键特征。HMT框架的一个潜在缺点是需要计算昂贵的迭代训练。在本文中，我们描述了两个减少参数的HMT模型，它们捕获了大量真实世界图像的一般结构。在图像HMT （iHMT）模型中，我们使用了这样一个事实，即对于大类别的图像，HMT的结构在尺度上是自相似的。这允许我们将iHMT的复杂性降低到只有9个容易训练的参数。在通用HMT （uHMT）中，我们采用贝叶斯方法确定这9个参数。uHMT不需要任何形式的培训。虽然简单，但我们通过一系列图像估计/去噪实验表明，这两个新模型几乎保留了由完整HMT建模的所有关键结构。最后，我们提出了一种快速移位不变的HMT估计算法，该算法在均方误差和视觉度量方面优于当前文献中所有其他基于小波的估计算法。
Wavelet-domain hidden Markov models have proven to be useful tools for statistical signal and image processing. The hidden Markov tree model captures the key features of the joint density of the wavelet coefficients of real-world data. One potential drawback to the HMT framework is the need for computationally expensive iterative training. In this paper, we prose two reduced-parameter HMT models that capture the general structure of a broad class of real-world images. In the image HMT (iHMT) model we use the fact that for a large class of images the structure of the HMT is self-similar across scale. This allows us to reduce the complexity of the iHMT to just nine easily trained parameters. In the universal HMT (uHMT) we take a Bayesian approach and fix these nine parameters. The uHMT requires no training of any kind. While simple, we show using a series of image estimation/denoising experiments that these two new models retain nearly all of the key structure modeled by the full HMT. Finally, we propose a fast shift-invariant HMT estimation algorithm that outperforms all other wavelet- based estimators in the current literature, both in mean- square error and visual metrics.