基于分数阶和低秩正则化的图像增强模型  

Image Enhancement Model Based on Fractional-order and Low Rank Regularization

作　　者：陈宝 唐玉超 丁效华[3] CHEN Bao;TANG Yu-chao;DING Xiao-hua(School of Mathematics and Information Sciences,Nanchang Hangkong University,Nanchang 330063,China;School of Mathematics and Information Sciences,Guangzhou University,Guangzhou 510006,China;Department of Mathematics,Harbin Institute of Technology,Shandong Weihai 264209,China)

机构地区：[1]南昌航空大学数学与信息科学学院,南昌330063 [2]广州大学数学与信息科学学院,广州510006 [3]哈尔滨工业大学数学系,山东威海264209

出　　处：《南昌航空大学学报（自然科学版）》2024年第2期18-29,共12页Journal of Nanchang Hangkong University(Natural Sciences)

基　　金：国家自然科学基金(12061045);江西省自然科学基金(20224ACB211004);南昌航空大学博士启动金(EA202307255)。

摘　　要：现有的弱光图像增强方法大多是基于整数阶微分进行计算的,这会引起纹理细节丢失。而且大多数弱光图像都具有潜在的噪声,在弱光图像增强的过程中,噪声也会随之被放大。为解决弱光图像增强过程噪声被放大的问题,对图像的反射层进行研究,提出通过添加低秩正则项来抑制弱光图像中的重噪声。此外,添加分数阶梯度到Retinex分解过程,使得弱光图像增强的同时能够保持图像的纹理细节部分。结果显示,所提出模型的特征相似度指数度量(FSIM)提高了2%,只评估亮度的基于自回归的图像清晰度度量(ARISMC1)和同时评估亮度与色彩的基于自回归的图像清晰度度量(ARISMC2)均提高了20%。与几种经典的弱光图像增强方法相比,所提出的方法在定性评估和定量指标方面均表现优异。The existing low light image enhancement methods are mostly caculated based on integer order differentiation,which can lead to the loss of textural details.Moreover,most low light images have potential noise,which is amplified during the enhancement process of low light images.To solve the problem of noise amplification during low light image enhancement,the reflection layer of the image is researched,and a low rank regularization term is proposed to suppress heavy noise in low light images.In addition,adding fractional order gradient to the Retinex decomposition process enables the preservation of texture details in the image while enhancing low light images.The experimental results show that the feature similarity index measure(FSIM)of the proposed model has been improved by 2%,the autoregressive based image sharpness metric(ARISMC1)that only evaluates brightness and the autoregressive based image sharpness metric(ARISMC2)that simultaneously evaluates brightness and color have both been improved by 20%.Compared with several classic low light image enhancement methods,the proposed method shows better performance in both qualitative evaluation and quantitative metrics.

关 键 词：图像增强 低秩 分数阶梯度 RETINEX 

分 类 号：O29[理学—应用数学]