关键词: 图像复原, 高斯混合模型, 分层贝叶斯, 马式距离

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