Abstract:

In recent years, Bayesian approach using Gaussian model as a patch prior has achieved great success in image denoising. However, this approach is not stable in solving inverse problems beyond denoising. A hierarchical Bayesian-based Gaussian mixture model is proposed to model image patch. Using the prior knowledge of the model parameters, the probability distribution of the mean and covariance matrices are modelled by the Gaussian-Wishart distribution，which makes the patch estimation process more stable. Based on the coherence of neighboring patches, the set of similar patches in the window can be derived by the multivariate Gaussian probability distribution of specific mean and covariance. The similarity is measured by the L2-norm metric, which is accelerated by using the summed square image and fast Fourier transform. The aggregation weights are based on the Gaussian distribution similarity with Mahalanobis distance, which are combined with the Gaussian similarity of the spatial domain on the image. The statistical characteristics of the natural image are better fitted. The experimental results for solving image restoration problem demonstrate the capabilities of the proposed method.

Key words: image restoration, Gaussian mixture model, hierarchical Bayesian, Mahalanobis distance

摘要：

近年来使用高斯模型作为块先验的贝叶斯方法取得了优秀的图像去噪性能，但是这一方法在去噪之外的逆问题求解方面性能不太稳定。提出一种基于分层贝叶斯的高斯混合模型对图像块建模，对模型参数引入先验知识，利用Gaussian-Wishart分布对均值和协方差矩阵的概率分布建模，使得块估计过程更加稳定。基于邻近块的相干性，利用L2范数度量完成局部窗口中相似块的聚类，局部窗口相似块利用特定均值和协方差的多元高斯概率分布建模，利用累加平方图及快速傅里叶变换的数值优化方法，加快相似性度量的计算时间。使用基于马式距离的高斯分布相似度的聚合权重，结合图像上的空间域高斯相似度，更好地拟合自然图像的统计特性。通过实验验证了提出的模型在图像复原求解中的有效性。

关键词: 图像复原, 高斯混合模型, 分层贝叶斯, 马式距离