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：
10.1109/83.931100
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发表时间：
2001-07-01
影响因子：
10.6
通讯作者：
Baraniuk, RG
中科院分区：
文献类型：
--
作者：
Romberg, JK;Choi, H;Baraniuk, RG
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（HMT）模型捕捉真实世界数据的小波系数的联合概率密度的关键特征。HMT框架的一个潜在缺点是需要计算上昂贵的迭代训练来将HMT模型拟合到给定的数据集（例如，使用期望最大化算法）。在本文中，我们大大简化了HMT模型，利用现实世界中的图像固有的自相似性。简化模型仅用9个元参数指定HMT参数（独立于图像的大小和小波尺度的数量），我们还引入了一个贝叶斯通用HMT（uHMT），它固定了这九个参数，uHMT不需要任何类型的训练，虽然非常简单，我们使用一系列图像估计/去噪实验表明，这些新模型几乎保留了由完整HMT建模的所有关键图像结构。最后，我们提出了一个快速的平移不变HMT估计算法，优于其他基于小波的估计在目前的文献中，无论是在视觉上和均方误差。
Wavelet-domain hidden Markov models have proven to be useful tools for statistical signal and image processing. The hidden Markov tree (HMT) model captures the key features of the joint probability density of the wavelet coefficients of real-world data. One potential drawback to the HMT framework is the need for computationally expensive iterative training to fit an HMT model to a given data set (e.g,, using the expectation-maximization algorithm). In this paper, we greatly simplify the HMT model by exploiting the inherent self-similarity of real-world images. The simplified model specifies the HMT parameters with just nine meta-parameters (independent of the size of the image and the number of wavelet scales), We also introduce a Bayesian universal HMT (uHMT) that fixes these nine parameters, The uHMT requires no training of any kind, While extremely simple, we show using a series of image estimation/denoising experiments that these new models retain nearly all of the key image structure modeled by the full HMT. Finally, we propose a fast shift-invariant HMT estimation algorithm that outperforms other wavelet-based estimators in the current literature, both visually and in mean square error.