Department of Electrical and Computer Engineering, Rice University, Houston, TX 77005, USA.
IEEE Trans Image Process. 2001;10(7):1056-68. doi: 10.1109/83.931100.
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). 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.
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）模型捕获了实际数据的小波系数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）。我们通过利用实际图像的固有自相似性极大地简化了 HMT 模型。简化模型仅用九个元参数指定 HMT 参数（与图像的大小和小波尺度的数量无关）。我们还引入了一种贝叶斯通用 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，但我们通过一系列图像估计/去噪实验表明，这些新模型保留了全 HMT 建模的几乎所有关键图像结构。最后，我们提出了一种快速平移不变 HMT 估计算法，在当前文献中的其他基于小波的估计器中，无论是在视觉上还是在均方误差方面都表现出色。
