目的 针对传统总变分方法在去除泊松噪声时容易出现“阶梯效应”和图像边缘模糊的问题，提出了一种基于分数阶变分的自适应去泊松噪声新模型。方法 一方面，新模型在分析了泊松噪声分布特点的基础上导出了非凸自适应正则项，它能够根据图像不同区域的特点自适应地调节正则项系数，以达到保持图像边缘的目的。另一方面，新模型利用分数阶离散微分向量能够结合更多图像信息的特点，将正则项中的一阶离散微分向量替换为分数阶离散微分向量，以此来达到抑制“阶梯效应”的目的。对于新模型的求解，结合交替迭代法和加权原始-对偶法提出了一种高效的数值解法。结果 数值实验结果表明，新模型明显优于传统总变分去泊松噪声模型，在有效抑制“阶梯效应”的同时图像边缘也得到了较好地保护，以经典的Peppers图片为例，新模型相比于传统模型，峰值信噪比(PSNR)由28.98提高到了30.24，图像结构相似度(SSIM)由0.77提高到了0.87。另外，所提的数值解法具有收敛速度快、复杂度低的特点，收敛时间从偏微分方程、Chambolle投影等传统数值解法的0.5与0.1秒缩短至0.056秒。结论 实验结果表明所提模型与数值解法的可行性，模型与数值解法在主要客观评价指标和图像视觉效果方面均优于传统的变分去泊松噪声模型，且模型与数值解法具有较好的普适性。但是模型中分数阶的阶次选取有待进一步优化。
Adaptive fractional-order variation model and algorithm forpoisson noise removal
Xie Bin,Liu Zhuan,Ding Cheng Jun(College of information engineering,Jiangxi University of Science and Technology)
Objective According to the problem that the traditional total variation method is prone to the staircase effect and the image edge blurring when removing the Objective According to the problem that the traditional total variational method is prone to the staircase effect and image edge blurring when the Poisson noise is removed, a new adaptive de-Poisson noise model based on fractional order variance is proposed. Methods On the one hand, the new model derives the non-convex adaptive regularization on the basis of analyzing the distribution characteristics of Poisson noise, which can adaptively adjust the regularization coefficients according to the characteristics of different regions of the image in order to achieve the purpose of preserving the edge of the image. On the other hand, the new model can use the fractional discrete differential vector to combine the more characteristics of image information, and replace the first order discrete differential vector in the regularization with the fractional discrete differential vector, so as to achieve the purpose of suppressing the staircase effect. For the solution of the new model, an efficient numerical method is proposed by combining the iteration method and the weighted primitive-dual method. Results The numerical experiment results show that the proposed model is obviously superior to the traditional total variation to the Poisson noise model. In the case of effectively suppressing the staircase effect, the edge of the image is also protected well. Taking the Peppers image with the new model as an example, compared with the traditional model, the peak signal to noise ratio (PSNR) increased from 28.98 to 30.24 and the image structure similarity (SSIM) increased from 0.77 to 0.87. In addition, the proposed numerical solution has the characteristics of fast convergence and low complexity. The convergence time is shortened from 0.5 or 0.1 seconds to 0.056 seconds by the traditional numerical solution of partial differential equation and Chambolle projection. Conclusion The experimental results show that the feasibility of the proposed model and numerical solution. The proposed model and numerical solution are both superior to the traditional variational Poisson noise model in the main objective evaluation index and image visual effect, and which have the better universality. But the order selection of the fractional order in the proposed model needs to be further optimized.