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本科毕业设计(论文)

题 目:

学 院: 专 业: 班 级: 学 号: 学生姓名：指导教师:

图像去模糊算法对比分析研究 职称:

二○一五年六月一日

图像去模糊算法分析与研究

摘 要

在数字时代，图像去模糊作为图像复原技术的一个分支，一直是一个具有挑战和吸引力的问题，具有重大的研究价值与社会意义。图像去模糊技术近年来得到了广泛研究，在理论和算法上也愈加系统和成熟，根据图像模糊核是否已知，图像去模糊技术被分为非盲图像去模糊和盲图像去模糊两大类。文章主要是选取几种典型的去模糊算法，在已知模糊核的基础上进行分析研究各算法的特点与去模糊效果的优劣性，即非盲去模糊算法的分析研究。基于运动模糊和离焦模糊这两大模糊类型，对其分别在有噪声（本文指高斯白噪声）和无噪声情况下的实验结果进行分析比较。

文章首先介绍了两种主要模糊图像类型及其造成图像模糊的成因，并对各模糊类型的点扩散函数估计获取。其次，是对图像基本退化模型的引入，从本质上了解图像模糊与去模糊的实质。接着，我们介绍了两类典型的去模糊评价方法：峰值信噪比（Peak Signal to Noise Ratio）和平均结构相似性指数（Mean Structural Similarity Index）。在这之后主要是算法比较，分类对几种典型的去模糊算法进行数学分析与讨论，包括用于去除运动模糊的Richardson-Lucy算法（即RL算法）和约束最小二乘法；用于去除离焦模糊的逆滤波算法和维纳滤波算法（Wiener filtering）。最后对几种算法进行Matlab仿真实验设计，并对其结果与恢复效果分析总结。

关键词：离焦模糊；运动模糊；点扩散函数；算法比较；仿真设计

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Abstract

In digital times, image de-blurring as a branch of image restoration technology has been a hard and attractive problem. However, image restoration has great value of the research and social significance. Image de-blurring technique has been widely studied in recent years and becomes more systematic and mature in theory and algorithm. According to the image blur kernel is known or not, de-blurring technique is divided into non-blind and blind image restoration. This article is mainly selecting several typical de-blurring algorithms, we make the analysis on the characteristics of each algorithm and the effect of the de-blurring based on the known blur kernel, in a word, the non-blind de-blurring algorithm analysis. Based on the Motion blurring and Defocus blurring types, we analysis and compare the experimental results in the case of noise (Gaussian noise) and no noise

The article analyzes two main kinds of blurred image types and the causes of blurring, and also introduces the types of the Point Spread Function and their estimation. Secondly, the article elaborates the basic image degradation model. So, we can understand the nature of the blurred images and the essence of the de-blurring. Then, it introduces two typical kinds of evaluation methods in the de-blurred image area: Peak signal to noise ratio (PSNR) and The mean structural similarity index (MSSIM).After that, we make a mathematical analysis and discussion for several typical de-blurring algorithms. It includes Richardson-Lucy algorithm (RL) and Constrained least squares method used to remove motion blur. Inverse filtering and Wiener filtering algorithm (WF) used to remove defocus blur. Finally, designing simulation experiments on several algorithms and summarizing the results, the recovery effect analysis included.

Keyword: Motion blur； Defocus blur； Point Spread Function

Algorithm comparison; Simulation design

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目 录

1绪论 .............................................................................. - 1 -

1.1论文研究目的和意义 .......................................................... - 1 - 1.2 图像去模糊技术的国内外研究现状 ............................................. - 1 - 1.3 主要研究内容及章节安排 ..................................................... - 4 - 2图像去模糊理论基础 ................................................................ - 5 -

2.1 模糊图像成因 ............................................................... - 5 -

2.1.1运动模糊 .............................................................. - 5 -

2.1.2离焦模糊 .............................................................. - 5 - 2.2 图像基本退化模型 ........................................................... - 5 - 2.3 图像去模糊评价方法 ......................................................... - 6 -

2.3.1 峰值信噪比（PSNR） ................................................... - 7 - 2.3.2 平均结构相似性指数（MSSIM） .......................................... - 7 - 2.5 本章小结 ................................................................... - 8 - 3算法比较 .......................................................................... - 9 -

3.1 运动模糊去除方法 ........................................................... - 9 -

3.1.1 运动模糊图像的退化模型及参数估计 ..................................... - 9 - 3.1.2 RL算法（Richardson-Lucy algorithm） ................................. - 10 - 3.1.3 约束最小二乘法 ...................................................... - 12 - 3.2 离焦模糊去除方法 .......................................................... - 14 -

3.2.1 离焦模糊图像的退化模型及参数估计 .................................... - 14 - 3.2.2 逆滤波复原 .......................................................... - 15 - 3.2.3 维纳滤波（Wiener filtering） ........................................ - 16 - 3.3 本章小结 .................................................................. - 19 - 4仿真实验与结果分析 ............................................................... - 20 -

4.1 仿真实验 .................................................................. - 20 - 4.2 运动模糊去除评价 .......................................................... - 20 -

4.2.1 运动模糊图像仿真 .................................................... - 20 -

4.2.1.1 RL算法仿真 .................................................... - 20 - 4.2.1.2 约束最小二乘仿真 .............................................. - 20 - 4.2.2 运动模糊去除效果和数据分析 .......................................... - 21 - 4.3 离焦模糊去除评价 .......................................................... - 24 -

4.3.1 离焦模糊图像仿真 .................................................... - 24 -

4.3.1.1 逆滤波法仿真 .................................................. - 24 - 4.3.1.2 维纳滤波仿真 .................................................. - 24 - 4.3.2 离焦模糊去除效果和数据分析 .......................................... - 24 - 4.4 本章小结 .................................................................. - 28 - 5结束语 ........................................................................... - 29 -

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5.1 总结 ...................................................................... - 29 - 5.2 展望 ...................................................................... - 29 - 致 谢 ............................................................................ - 31 - 参考文献 .......................................................................... - 31 -

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