## 基于曲率的图像泊松去噪模型及方法

Title     Image poisson denoising based on  Euler’s elatica and curvature
Abstract
In our daily lives, images play an important role. Compared with the words, they have many merits, such as, easier to understand, more direct to read and with the lager capacity of carrying of a large mount of information. However, in the imaging, transmission and storage process of the images, they often suffer from the interference of varieties of noise.So image denoising has become a very fundamental and critical work. As to the Gaussian noise,there are many works about how to build the denoising model and find their solve.However, in the imaging process of , such as X-ray images, astronomical images, most of them will suffer from quantum noise over the changing of time or space . Such noise is no longer additive noise, because its probability density follows the Poisson distribution. So,we call it Poisson noise. Therefore, the denoising of Poisson noise is a very important and tough work. Inspired by the denoising of Gaussian noise with Euler elastic model based on curvature, we established the Euler elastic denoising model based on curvature to deal with the Poisson noise, and find out the numerical solution of the model.Then, we have the corresponding numerical experiments.

Keywords :  curvature    image denoising   Euler elastica model   piosson noise

1  绪论 •1
1.1 背景知识及研究意义1
1.2 本文主要研究内容2
2  现有图像Poisson去噪方法研究现状•3
2.1 方差稳定转换方法3
2.2 基于TV的 Poisson去噪方法4
2.3 更多的 Poisson去噪方法•5
3  基于曲率的图像泊松去噪模型•7
3.1 曲率与欧拉弹性7
3.2 欧拉弹性的泊松去噪模型9
3.3 模型数值解法10
3.4 数值实验与结果15

1  绪论

1.1  背景知识及研究意义

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