摘 要

摘 要

图像去噪即从一张带有噪声的图像中去除其中所包含的附加噪声。本文主要研究基于稀疏表达的高斯噪声和椒盐噪声去噪模型与算法。由于高斯噪声和椒盐噪声特性的不同，我们分别对高斯噪声和椒盐噪声建立了模型。使得针对不同的噪声应用相应的模型处理可以得到更好的去噪效果。

首先，我们学习与研究基于稀疏表达的高斯噪声图像模型。该类算法和模型的基本思想是将原始图像表达为局部的基元线性组合，并约束线性组合系数的稀疏性，从而建立解决去噪问题的能量函数，在极小化过程中通过OMP和K-SVD算法优化该能量函数。在实现中，我们可以用离散余弦变换（DCT）构造其中的基元组，也可以自适应的学习该基元组。我们实现了该算法，并应用于高斯噪声图像的去噪问题。

另一方面，我们研究椒盐噪声的图像去噪问题。我们发现，应用经典的稀疏表达模型会在处理去除椒盐噪声图像中失效，因此我们提出一种新的基于稀疏性的椒盐噪声图像去噪模型。结合椒盐噪声的特性，我们用更为鲁棒的带权稀疏表达模型，在使用基元组时采用DCT基元组，并通过OMP方法优化该稀疏表达模型。通过实验表明，该方法相对于经典的稀疏表达模型能更好的去除椒盐噪声。

关 键 词：图像去噪；基元表示；OMP；K-SVD；稀疏编码

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西安交通大学本科毕业设计（论文）

ABSTRACT

Image denoising is to remove the noises from a given observed noisy image. This paper mainly concentrates on how to remove Gaussian noises and pepper noises based on image sparse representation. Based on the characteristics of Gaussian noises and pepper noises, we learned and proposed the sparse representation based denoising model and algorithms to achieve image denoising.

Firstly, we learn and investigate the sparse representation based Gaussian noise removal. The main idea is to represent the image by the local sparse linear combination over a dictionary of basis, and then OMP and K-SVD methods are used to optimize the deduced energy function. In implementation, the dictionary of basic can be set as constant or learned adaptively from the noisy images. We implemented this model and applied it to Gaussian noise removal.

Secondly, we investigate the pepper noise removal based on image sparse representation. We find that, the traditional sparse representation model cannot handle the pepper noise removal problem perfectly. In this paper, we propose a novel weighted sparse representation model to remove the pepper noises, which uses the dictionary of DCT basis and optimize it by OMP algorithm. Experiments show that this proposed method can accurately remove pepper noises with much higher Peak Signal to Noises Ratio (PSNR).

KEY WORDS: Image denoising;Dictionary learing;OMP;K-SVD;Sparse coding

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目录

目 录

1 绪论 .................................................................. 1 1.1 研究背景 .......................................................... 1 1.2 本文主要研究工作 .................................................. 2 2 基于稀疏线性表达的高斯噪声去噪模型 .................................... 4 2.1 模型介绍 .......................................................... 4 2.1.1 局部块上建立去噪模型 ........................................... 4 2.1.2 图像整体上建立去噪模型 ......................................... 5 2.2 模型优化求解 ...................................................... 6 2.2.1 采用DCT基元组优化模型 ......................................... 6 2.2.2 全局学习基元组优化模型 ......................................... 7 2.2.3 自适应学习基元组优化模型 ....................................... 7 2.3 迭代求解算法 ...................................................... 8 3 基于稀疏线性表达的椒盐噪声去噪模型 .................................... 2 3.1 模型的建立 ........................................................ 2 3.2 模型优化求解 ...................................................... 3 3.3 迭代求解算法 ...................................................... 5 4 实验 .................................................................. 6 4.1 高斯噪声去噪实验 .................................................. 7 4.2 椒盐噪声去噪实验 .................................................. 8 5 结论与展望 ........................................................... 10 参考文献 ............................................................... 11 附 录 ................................................................. 12 致 谢 ................................................................. 25

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西安交通大学本科毕业设计（论文）

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