基于Lp收缩算子的改进广义全变分去噪方法

Improved Generalized Total Variation Denoising Method Based on Lp Shrinkage

二阶广义的全变分模型是一种建立在全变分模型的思想之上进行改进的图像去噪模型,该模型是一种考虑了一阶以及高阶梯度稀疏性的模型,能够有效地抑制阶梯伪影效应的产生。Lp收缩算子相比于L1算子增加了一个自由度,它能够更好地刻画稀疏梯度信息,同时Lp收缩算子的等高线对噪声更加鲁棒。考虑到Lp收缩算子的优势,将Lp收缩算子引入二阶广义全变分去噪模型,提出改进的二阶广义全变分Lp收缩算子模型(TGV2-Lp)。利用交替乘子迭代法对模型进行求解,引入快速傅里叶算法提高算法效率。通过测试6组图片、对比传统的3种去噪模型,从实验结果可以得出,提出的模型TGV2-Lp在有效保留图片边缘细节信息的同时,能够有效去除噪声,在视觉效果、峰值信噪比和结构相似性都有一定优势.

Second-order total generalized variation model is an image denoising model based on the idea of the total variation(TV)model.Both the first-order and high-level sparseness are taken into account so that the generation of the stair-case artifact of TV is effectively suppressed.The Lp shrinkage adds a degree of freedom compared to the L1 operator,which better describes the sparse gradient information,while the contours of the Lp shrinkage are more robust to noise.Considering the advantages mentioned above,we introduce the Lp shrinkage in second-order total generalized variation model and propose second-order total generalized variation with Lp shrinkage(TGV2-Lp)model.The model is solved by the alternating multiplier iteration method.The fast Fourier transform algorithm is introduced to further improve the efficiency of the algorithm.By testing six sets of pictures and comparing the traditional three denoising models,it can be concluded from the experimental results that the proposed model can effectively remove noise while effectively retaining the edge details of the processed picture and has certain advantages in visual effects,peak signal-to-noise ratio,and structural similarity.