【作者】 王媛；

【导师】 庞志峰；

【作者基本信息】 河南大学 ， 统计学， 2020， 硕士

【摘要】 在成像的过程中,受光源或物体表面反光等因素的影响,采集到的图像经常会出现光照不均匀的现象,比如出现过暗区域或者过亮的区域.在一定程度上这种光照不均匀会改变图像的原始面貌,从而带来较差的视觉效果,并且也不利于后续的图像处理.Retinex技术可以使感兴趣的部分更加突出,使处理后的图像更适合观察或易于其它工程应用.基于全变分(Total Variation,TV)型泛函空间,本文提出一种新型的非凸Retinex模型,并利用有效的数值方法进行求解.其主要内容如下:·为了更好地刻画图像的稀疏性,基于非凸TV型正则化提出一个新的图像Retinex模型,其中数据拟合项和正则项是基于指数变换的,因此能有效地描述图像细节.尤其在模型中,基于非凸全变分?p(拟)范数(p∈(0,1))的正则项是用来惩罚分段常数的稀疏性,基于非凸高阶全变分?q(拟)范数(q∈(0,1))的正则项是用来惩罚空间光滑区域.·由于所提出的模型是非凸、非光滑和非Lipschitz的,所以文中利用交替极小化(Alternating Minimization,AM)方法求解原问题,然后利用交替方向乘子法(Alternating Direction Method of Multipliers,ADMM)和迭代加权?1算法(Iteratively Re-weighted?1Algorithm,IRLA)求解对应的子问题.此外,本文讨论所提模型的一些数学性质和数值算法.最后,将模型用于处理仿真图像和真实图像,通过与其它几种Retinex变分模型相比,其实验结果无论在视觉上还是量化准则上都展示出所提模型的有效性和鲁棒性.更多还原

【Abstract】 In the imaging process,due to the effect of the light source or the reflection of the surface of the object and other factors,non-uniform illumination often occurs in the acquired images,such as underexposure areas and overexposure areas.To some extent,illumination inhomogeneity changes the original appearance of the image,resulting in poor visual effect,and is not conducive to the subsequent image processing.Retinex technology can make the interesting part more prominent,so that the processed images are more suitable for observation or other engineering applications.Based on total variation(TV)type functional space,this paper proposes a new non-convex Retinex model and solves it by effective numerical method.The main contents are as follows:· In order to more effectively describe the sparsity of the image,we propose a new image retinex model based on the non-convex total variation(TV)-type regularization,where the data fitting term and regularization term based on the exponent transform are used to describe image details efficiently.Especially in the model,one regularization term based on the non-convex total variation ?pquasi-norm with p ∈(0,1)is used to penalize the sparsity of the piecewise constants and one regularization term based on the non-convex high-order total variation ?qquasi-norm with q ∈(0,1)is used to penalize the piecewise smoothing regions.· Since the proposed model is non-convex,non-smooth and non-Lipschitz,we employ the alternating minimization(Alternating Minimization,AM)method,where the iteratively re-weighted ?1algorithm(Iteratively Re-weighted ?1Algorithm,IRLA)and the alternating direction method of multipliers(Alternating Direction Method of Multipliers,ADMM)are used in the sub-minimization problems.In addition,this paper discusses some mathematical properties of the proposed model and numerical algorithm.Finally,experiments on the simulated and real images illustrate the effectiveness and the robustness of our proposed model both visually and quantitatively by compared with some Retinex variational models.更多还原