图像方向纹理保持的方向全变差正则化去噪模型及其主优化算法

摘要

The regularization method has recently been an efficient approach to make the process of image denoising well-posed ,while preserving image textures and details become more intractable .This paper focused on directional texture preserving im-age denoising problem gives a directional texture preserving total variation regularization based model .Furthermore ,we analyze and demonstrate some equivalent properties of the directional total variation ,and give the majorization minimization algorithm based on iteratively constructing surrogate functionals and B-spline difference filters .Numerical experiments show that the new method can achieve better result in removing the noise ,restraining staircase effect and preserving directional texture .%正则化方法是目前解决图像去噪不适定性的一条有效途径，但对于图像中纹理细节的保持仍是棘手的问题。本文针对图像方向纹理保持的去噪问题，给出了图像方向纹理保持的方向全变差正则化去噪模型。分析和证明了方向全变差的若干等价表示性质，并基于该性质迭代构造代理泛函和B样条离散差分逼近方法，给出了一种主优化去噪算法。数值实验表明，该方法在去除噪声、抑制图像的“阶梯效应”和保持图像方向纹理等方面取得较好的效果。