各向异性张量加权分数阶变分图像去噪模型
Anisotropic Tensor Weighted Fractional-Order Variation Image Denoising Model
摘要: 为了增强去噪后图像的边缘和保留图像纹理，本文提出了一种新的各向异性张量加权分数阶变分图像去噪模型，即利用分数阶的Jacobian矩阵形式与一个各向异性张量的乘积的Frobenius范数，作为本文模型的正则化子，其包含图像在每个像素点的局部邻域变化的信息，根据图像结构灵活地控制和定向去除噪声，增强图像的边缘和保留纹理细节信息。本文采用交替方向乘子(ADMM)法进行数值求解，所有的子问题都具有闭形解。数值实验表明，该模型复原的图像有效地保留图像的边缘和纹理等细节特征，抑制阶梯效应，与其他模型相比更具有竞争力。
Abstract: In order to enhance the edge of the denoised image and preserve the texture of the image, a new anisotropic tensor weighted Fractional-order Variation image denoising model is proposed in this paper, which uses the Frobenius norm of the product of fractional Jacobian matrix form and an anisotropic tensor as the regularizer of this model. It contains the local neighborhood change information of the image at each pixel point, and can flexibly control and directionally remove noise and enhance edge according to the image structure, and retain texture details. In this paper, alternate directional multipliers method (ADMM) is used to solve numerical problems. Numerical experiments show that this model can effectively retain the edge and texture of the image and suppress the step effect, which is more competitive than other models.
文章引用：王佳佳, 唐利明. 各向异性张量加权分数阶变分图像去噪模型[J]. 图像与信号处理, 2022, 11(3): 162-181. https://doi.org/10.12677/JISP.2022.113017

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