Portilla Javier, Strela Vasily, Wainwright Martin J, Simoncelli Eero P
Dept. of Comput. Sci. and Artificial Intelligence, Univ. de Granada, Spain.
IEEE Trans Image Process. 2003;12(11):1338-51. doi: 10.1109/TIP.2003.818640.
We describe a method for removing noise from digital images, based on a statistical model of the coefficients of an overcomplete multiscale oriented basis. Neighborhoods of coefficients at adjacent positions and scales are modeled as the product of two independent random variables: a Gaussian vector and a hidden positive scalar multiplier. The latter modulates the local variance of the coefficients in the neighborhood, and is thus able to account for the empirically observed correlation between the coefficient amplitudes. Under this model, the Bayesian least squares estimate of each coefficient reduces to a weighted average of the local linear estimates over all possible values of the hidden multiplier variable. We demonstrate through simulations with images contaminated by additive white Gaussian noise that the performance of this method substantially surpasses that of previously published methods, both visually and in terms of mean squared error.
我们描述了一种基于超完备多尺度方向基系数统计模型的数字图像去噪方法。相邻位置和尺度的系数邻域被建模为两个独立随机变量的乘积：一个高斯向量和一个隐藏的正标量乘数。后者调制邻域中系数的局部方差，因此能够解释经验观察到的系数幅度之间的相关性。在此模型下，每个系数的贝叶斯最小二乘估计简化为隐藏乘数变量所有可能值上局部线性估计的加权平均值。我们通过对受加性高斯白噪声污染的图像进行模拟表明，该方法的性能在视觉上和均方误差方面都大大超过了先前发表的方法。
