一种去除Gamma乘性噪声的全变分模型

A Novel Total Variational Model for Gamma Multiplicative Noise Removal

针对现有的去除图像乘性噪声变分模型存在"阶梯效应"和图像模糊等问题,提出了一种具有严格凸性的去除图像Gamma乘性噪声的全变分新模型。首先,通过分析Gamma噪声的数学特征,采用最大似然估计方法和贝叶斯公式导出了全变分模型的保真项,引入协调项,并利用一种新颖的混合测度构造了新的模型。再使用交替迭代最优化算法,给出了数值解,并从理论上证明了该迭代序列的收敛性。实验结果表明,本模型有很好的去噪效果,在有效抑制图像中的"阶梯效应"的同时能更多地保留图像的纹理细节特征。

A novel total variational model with strict convexity was proposed to solve the problem that the＇ step-casing effect＇ and image blurring are always with the existing variational models for multiplicative noise removal. Firstly, the fidelity term of the modified model was derived by applying the maximum likelihood estimate method and the Bayesian formulation. Then, the new total variational modal was developed by combining the fidelity term, a fitting term and a hybrid measurement. An alternating minimization algorithm was used to find out the minimizer of such an objective function and proved the convergence for the variational problem. Finally, the numerical ex- periments showed that the texture details in the denoised images are kept and the ＇ step-casing effect＇ is suppressed.