基于梯度旋转的局部分块图像重建方法研究

论文总字数：25863字

摘 要

图像重建是图像处理中的重要问题之一。边缘保持的图像重建可看作是跳跃曲面估计问题。为了进行有效的图像重建，基于非参数回归方法提出梯度旋转的局部分块图像重建方法。

本文以跳跃回归分析方法作为理论基础进行图像重建，提出了梯度旋转的改进思路，将梯度方向旋转45度后将待估计点的邻域划分成四个子邻域，再在每个子邻域中进行局部分块线性核回归，并将此方法与已有的局部四象限回归方法和按梯度局部两象限回归方法进行比较。研究发现梯度旋转的局部分块图像方法在有效去除图像噪声的同时能够很好的保持图像边缘特性。数值模拟实验和实际图像分析显示了本文方法的优越性和有效性，并且有一定的应用价值。

关键词：图像重建，图像去噪，边缘保持，核回归，局部多项式回归

LOCAL BLOCK-WISE IMAGE RECONSTRUCTION BASED ON GRADIENT ROTATION

Abstract

Image reconstruction is one of the most important problems in the image processing. Edge-preserving image reconstruction is actually the problem of jumping surface estimation. To solve the limit of traditional regression estimation function obtained at the jump point of having no statistical consistency, a procedure is proposed based on nonparametric regression methods by using the idea of gradient-rotating local block-wise neighborhood.

This paper takes jump regression analysis as a theoretical basis for image reconstruction, proposing the idea of the gradient-rotation. After the rotated 45 degrees of the gradient of the given point, the neighborhood of the given point will be divided into four sub-neighborhood, then the local linear kernel regression work in each sub-neighborhood. The existing method will be compared, such as the local four quadrants regression and local two-quadrant regression with gradient. It is found that gradient-rotating local block-wise image restoration method can effectively remove image noise while preserving the feature of image edges. Numerical experiments and real image analysis showed the superiority and effectiveness of the method, and it will have some practical value.

KEY WORDS: image reconstruction, image denoising, edge-preserving, kernel regression, local polynomial regression

目 录

摘要 ……………………………………………………………………………………………Ⅰ

Abstract …………………………………………………………………………………… Ⅱ

1. 引言 …………………………………………………………………………………3

1.1 研究背景 ……………………………………………………………………………3

1.2 研究现状 ……………………………………………………………………………3

1.3 研究内容 ……………………………………………………………………………4

1. 模型研究 ………………………………………………………………………4

2.1 局部分段线性核回归 ………………………………………………………………4

2.2 局部四象限回归 ……………………………………………………………………6

2.3 按梯度局部两象限回归………………………………………………………………7

第三章 梯度旋转算法研究 …………………………………………………………………9

3.1 梯度旋转的局部四象限回归 ………………………………………………………9

3.2 关于阈值的选择 ……………………………………………………………………11

3.3 关于参数的选择 ……………………………………………………………………12

第四章 数值模拟实验 ……………………………………………………………………12

4.1 数值模拟实验一 ……………………………………………………………………13

4.2 数值模拟实验二 ……………………………………………………………………14

4.3 数值模拟实验三 ……………………………………………………………………16

4.4 数值模拟实验四 ……………………………………………………………………17

第五章 实际图像分析 ………………………………………………………………………19

5.1 lena图像的实验研究 ………………………………………………………………19

5.2 house图像的实验研究 ………………………………………………………………21

5.3 cameraman图像的实验研究 ………………………………………………………22

第六章 结论与改进方向 ……………………………………………………………………24

第七章 附录 ………………………………………………………………………………25

致谢 ……………………………………………………………………………………………33

参考文献（References） ………………………………………………………………………34

第一章 引 言

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