STOCHASTIC RELAXATION, GIBBS DISTRIBUTIONS, AND THE BAYESIAN RESTORATION OF IMAGES
STOCHASTIC RELAXATION, GIBBS DISTRIBUTIONS, AND THE BAYESIAN RESTORATION OF IMAGES
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DOI：
10.1109/tpami.1984.4767596
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发表时间：
1984-01-01
影响因子：
23.6
通讯作者：
GEMAN, D
中科院分区：
文献类型：
--
作者：
GEMAN, S;GEMAN, D
我们在图像和统计力学系统之间做一个类比。像素灰度级以及边缘的存在和方向被视为晶格状物理系统中的原子或分子的状态。物理系统中能量函数的分配决定了它的吉布斯分布。由于吉布斯分布，马尔可夫随机场（MRF）的等价性，这种分配也确定了MRF图像模型。与MRF的局部特征相比，能量函数是体现图像属性的更方便和自然的机制。对于一系列退化机制，包括模糊、非线性变形以及乘性或加性噪声，后验分布是具有类似于图像模型的结构的MRF。以此类推，后验分布定义了另一个（假想的）物理系统。在物理系统中，温度的逐渐降低隔离了低能态（“退火”），或者说是吉布斯分布下最可能的状态。类似的操作下的后验分布产生的最大后验概率（MAP）估计的图像退化的意见。其结果是一个高度并行的"松弛"算法的MAP估计。我们建立的算法的收敛性能，我们实验与一些简单的图片，在低信噪比获得良好的解释。
We make an analogy between images and statistical mechanics systems. Pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice-like physical system. The assignment of an energy function in the physical system determines its Gibbs distribution. Because of the Gibbs distribution, Markov random field (MRF) equivalence, this assignment also determines an MRF image model. The energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the MRF. For a range of degradation mechanisms, including blurring, nonlinear deformations, and multiplicative or additive noise, the posterior distribution is an MRF with a structure akin to the image model. By the analogy, the posterior distribution defines another (imaginary) physical system. Gradual temperature reduction in the physical system isolates low energy states (``annealing''), or what is the same thing, the most probable states under the Gibbs distribution. The analogous operation under the posterior distribution yields the maximum a posteriori (MAP) estimate of the image given the degraded observations. The result is a highly parallel ``relaxation'' algorithm for MAP estimation. We establish convergence properties of the algorithm and we experiment with some simple pictures, for which good restorations are obtained at low signal-to-noise ratios.