Total variation (TV) theory of image for denoising effect is not ideal.To overcome the excessive smoothing of edge and blurred phenomenon and block effect after suppression of noise,we present a differential total variation model for image denoising based on the advantage of four derivative suppression to"staircase effect".First,we demonstrate the advantages and disadvantages of traditional denoising model and others.Then in order to better protect the image edge details,we propose a new adaptive TV model with edge indica-tor combining the theory of edge index with the four order total variation model.The edge index is used to design weight function of par-tial control,which makes the edge area and smoothing area of the image be different denoising effect,with relaxation descent method to find the solution to the established model.The experiments show that the proposed method can eliminate the image noise while suppress-ing the"staircase effect",and preserve effectively the edge details and texture information of the image.%全变差(TV)理论对图像降噪处理的效果不太理想,同时为了克服边缘的过度平滑和抑制降噪后图像易产生的"模糊现象"和"块状效应"的问题,在四阶导数对"阶梯效应"抑制优势的基础上,提出了一种基于四阶微分全变差的图像去噪模型.首先论证了传统的去噪模型及其他各阶去噪模型的优缺点;然后为了更好地保护图像边缘细节,将边缘指标的理论与四阶全变差模型相结合,提出了一个带有边缘指标的新的自适应TV模型,利用边缘指标设计分项控制权函数,使得图像的边缘区域和平滑区域具有不同的去噪效果,用松弛下降法对所建立模型进行求解.实验结果表明,该方法在去除图像噪声的同时,抑制了"阶梯效应"的产生,并有效地保留了图像的边缘细节及纹理信息.
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