基于小波域隐马尔可夫树模型的图像复原

Image Restoration Based on Wavelet-Domain Hidden Markov Tree Model

从图像复原的Bayesian方法出发,提出一种基于小波域隐马尔可夫树(HMT)模型的线性图像复原算法.小波域HMT模型采用混合高斯模型刻画各子带系数的概率分布,并通过小波系数隐状态在多个尺度之间的Markov依赖性来刻画自然图像小波系数随尺度减小而指数衰减的特性.由于小波域HMT模型准确刻画了自然图像小波变换的统计特性,该文算法以此作为自然图像的先验模型,将图像复原问题转化为一个约束优化问题并用最速下降法对其进行求解.同时,提出了一种规整化参数和HMT模型参数的自适应选择方法.实验结果表明,基于小波域HMT模型的图像复原算法较好地再现了各种边缘信息,复原出的图像在信噪比和视觉效果方面都有明显的提高.

From the viewpoint of Bayesian method for image restoration, a linear image restoration algorithm based on wavelet domain Hidden Markov Tree (HMT) model is proposed. Wavelet-domain HMT models the dependencies of multiscale wavelet coefficients through the state probabilities of the wavelet coefficients, whose distribution densities can be approximated by Gaussian mixture model. The proposed algorithm specifies the prior distribution of real-world images through wavelet-domain HMT model and converts the restoration problem to an constrained optimization task which can be solved with the steepest descend method. Parameters of the HMT model are adaptively determined through a fast estimation method which avoids the time-consuming training process. Experimental results show that the algorithm properly retrieves various kinds of edges and the PNSR and subjective visual effect of the restored images are improved significantly.