基于小波域双层贝叶斯模型的图像复原

Image restoration based on wavelet-domain double level Bayesian models

为了克服正交小波变换用于图像复原引起的振铃现象,提出了一种基于小波域双层贝叶斯模型的图像复原算法。采用移不变小波变换,经过简单的转换,使计算复杂度较正交小波变换法并没有显著增加。对于涉及小波系数和超参数的估计问题,通过双层贝叶斯模型方法解决。首先使用局部高斯分布作为第一层模型,主要用于刻画原始图像小波系数的先验分布;第二层模型用于对超参数的估计,假设局部逆方差为服从Gamma分布的随机变量。基于双层贝叶斯模型,采用最大后验概率估计(MAP)同时进行参数估计与图像复原,计算机实验验证了该方法的有效性。

Abstract： In this paper, an image restoration algorithm based on wavelet domain with double level Bayesian models was proposed. In order to overcome the ringing phenomena in image restoration, translation-invariant wavelet transform was adopted, instead of the orthogonal discrete wavelet transform （DWT）. At the same time, the computation complexity had less salient increase than that of the orthogonal DWT by simple transform. The estimation problem about original image wavelet coefficients and hyperparameter was solved by adopting a kind of double level Bayesian models. In the first level model, local Gaussian model was employed to specify original image coefficients prior distribution. In the second level model, the hyperparameter was estimated by regarding them as random variable obeying Gamma distribution Based on the double level models, maximum a posteriori （MAP） was adopted to simultaneously estimate the parameters and recover the image. At last, computer experiments prove that the proposed algorithm is very effective.