变指数变分乘性去噪模型的研究

发布时间：2019-05-22 21:27

【摘要】：图像去噪是图像处理中一项比较关键且困难的问题,它是进行大部分图像操作技术的前提,并且需要得到较高的准确性。基于偏微分方程方法的图像去噪技术已很成熟,得到众多专业人士青睐,取得了很大成功,其中,使用基于变分法的模型进行图像乘性噪声去噪方面已经产生很好的成果,且为之后的研究奠定了基础。本文主要的研究内容是提出了变指数变分乘性去噪模型,证明了模型解的存在唯一性和比较原理,同时证明了演化方程解的存在性、唯一性及其相关性质。最后,给出了模型及加速算法的实验结果,并与经典模型进行了对比分析。乘性噪声与标准高斯(Gauss)加性噪声产生方式不同,本文根据Gamma噪声模型特点使用变分法来去除乘性噪声。首先,本文针对Dong等人变分乘性去噪模型,通过利用图像灰度值和高斯梯度模改进了正则项,构造了正则项变指数使其介于全变分模型和L~2正则模型指数之间,达到了既可抑制阶梯效应去除噪声,又保留边界和图像信息自适应的效果。理论方面,在以上提出的变指数变分乘性去噪模型下,本文证明了该模型极小化问题解的存在性,将其解的存在性转化为泛函极小元存在性,利用泛函严格凸性证明解的唯一性,然后利用上述解存在唯一性和空间性质得出比较原理;针对相应的演化方程,为了克服方程奇性和退化问题,首先定义了各项异性变指数Sobolev空间,然后定义了弱解,正则化演化方程,得到了解的预估计进而解决了方程奇性问题,在对正则的方程弱解定义中取极限,证明了极限满足演化方程弱解定义,从而弱解存在性得到证明。本文利用了方程本身性质和Gronwall不等式证明了解的唯一性和比较原理。数值方面,给出了有限差分离散格式,通过MATALB软件使用有限差分法和快速显式扩散方法FED(Fast Explicit Diffusion)将其实现,与经典去噪模型进行对比,并进行了实验分析。实验结果表明,FED快速算法可以提高算法效率,该模型从实验时间和实现效果上均优于经典乘性去噪模型。
[Abstract]:Image de-noising is a key and difficult problem in image processing. It is the premise of most image manipulation technology, and it needs to get higher accuracy. The image de-noising technology based on the method of partial differential equation has been well-established and has been favored by many professionals. The main research contents of this paper are to put forward the variable-index variational-multiplicative de-noising model, and prove the existence and uniqueness of the model solution and the principle of the comparison. At the same time, the existence, uniqueness and related properties of the solution of the evolution equation are proved. Finally, the experimental results of the model and the acceleration algorithm are given and compared with the classical model. The multiplicative noise is different from the standard Gaussian (Gaussian) additive noise, and the variational method is used to remove the multiplicative noise according to the characteristics of the Gamma noise model. First, this paper, aiming at Dong et al. variational-multiplicative de-noising model, improves the regular term by using the image gray value and the Gaussian gradient mode, and constructs the regular term transformation index to be between the full-variational model and the L-2 regular model index, so that the step-effect removal noise can be suppressed, And preserving the self-adaptive effect of the boundary and the image information. In theory, in the above-mentioned variable-index variational-multiplicative de-noising model, this paper proves the existence of the solution of the minimal problem of the model, transforms the existence of the solution into the existence of a functional minimum element, and proves the uniqueness of the solution by using the strictly convex property of the functional, In ord to overcome that problem of singularity and degradation of the equation, we first define the Sobolev space of the anisotropy index, and then define the weak solution and the regularized evolution equation. It is proved that the existence of the weak solution is proved by the definition of the weak solution of the evolution equation. The uniqueness and the principle of the comparison of the property of the equation and the Gronwall inequality are used in this paper. In the numerical aspect, a finite difference discrete format is given, which is realized by using the finite difference method and the fast explicit diffusion method FED (Fast Explicit Diffusion) by the MATALB software, and compared with the classical de-noising model, and the experimental analysis is carried out. The experimental results show that the fast algorithm of FED can improve the efficiency of the algorithm, and the model is superior to the classical multiplicative de-noising model from the experimental time and the effect.
【学位授予单位】：哈尔滨工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TP391.41

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