In this paper, a new regularization term in the form of L1-norm based fractional gradient vector flow (LF-GGVF) is presented for the task of image denoising. A fractional order variational method is formulated, which is then utilized for estimating the proposed LF-GGVF. Overlapping group sparsity along with LF-GGVF is used as priors in image denoising optimization framework. The Riemann-Liouville derivative is used for approximating the fractional order derivatives present in the optimization framework. Its role in the framework helps in boosting the denoising performance. The numerical optimization is performed in an alternating manner using the well-known alternating direction method of multipliers (ADMM) and split Bregman techniques. The resulting system of linear equations is then solved using an efficient numerical scheme. A variety of simulated data that includes test images contaminated by additive white Gaussian noise are used for experimental validation. The results of numerical solutions obtained from experimental work demonstrate that the performance of the proposed approach in terms of noise suppression and edge preservation is better when compared with that of several other methods.

中文翻译：

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基于分数梯度向量流和重叠群稀疏性作为先验的图像去噪

在本文中，针对图像去噪任务，提出了一种新的基于 L1 范数的分数梯度向量流 (LF-GGVF) 形式的正则化项。制定了分数阶变分方法，然后将其用于估计所提出的 LF-GGVF。重叠组稀疏性与 LF-GGVF 一起用作图像去噪优化框架中的先验。Riemann-Liouville 导数用于逼近优化框架中存在的分数阶导数。它在框架中的作用有助于提高去噪性能。使用众所周知的乘法器交替方向法 (ADMM) 和分裂 Bregman 技术以交替方式执行数值优化。然后使用有效的数值方案求解得到的线性方程组。包括被加性高斯白噪声污染的测试图像在内的各种模拟数据用于实验验证。从实验工作中获得的数值解的结果表明，与其他几种方法相比，所提出的方法在噪声抑制和边缘保留方面的性能更好。