图像盲复原算法研究

发布时间：2018-04-28 06:57

  本文选题：图像盲复原 + 点扩散函数　； 参考：《吉林大学》2015年博士论文

【摘要】：作为图像处理领域的重要分支和研究热点之一,图像复原方法的研究始终具有重要理论意义和广泛的应用价值.在图像复原问题中,观测的退化图像通常可以简化为线性移不变卷积核与高斯白噪声之和,其数学模型可以写成：其中,u(x,y),g(x,y)和n(x,y)分别表示原始图像,退化图像和加性噪声,h(x,y)表示引起图像退化的点扩散函数(PSF),”*”表示卷积算子.大多数复原算法都是建立在点扩散函数已知的前提下,而在实际问题中,点扩散函数通常是未知的.因此对盲复原理论及算法的研究,有着理论意义与实际需求. 图像盲复原一直以来都是图像复原中比较困难的问题之一.针对图像盲复原问题,本文详细地介绍了其理论基础和主要算法.本文主要针对相机与所拍摄景物之间由于相对位置移动而使所获得图像发生运动模糊的情况,提出了有效的图像盲复原算法,主要工作如下： 1.提出了一种基于频域迭代和指导滤波的图像盲复原算法. 首先,在频域上估计点扩散函数.频域迭代公式为其中,F表示Fourier变换算子,F(.)*表示F的复共轭,α1和α2为常数.我们利用频域迭代法估计出PSF的近似解. 其次,将估计出的PSF的近似解作为初始值,此时图像盲复原问题变成了非盲复原问题.由于指导滤波能够在保持图像边缘不被模糊的前提下,有效地去除图像的噪声并抑制振铃效应.因此,应用基于指导滤波的复原算法恢复出目标图像初值. 指导滤波的函数表达式为：其中,u,和up分别表示指导图像和滤波图像,u表示滤波后的图像,ω是选择窗口的大小,ε0是正则化参数. 考虑下面两个函数其中,u。是预估计图像,λ0是正则化参数.将其解u,和up分别作为指导图像和滤波输入图像,利用指导滤波对图像up进行平滑以达到去噪的目的,进而得到更清晰的图像. 最后,将上述两部分交替迭代求解,可以得到最终的清晰图像. 2.提出了基于强边缘检测和指导滤波的图像盲复原算法. 首先,利用图像的强边缘信息来估计出点扩散函数PSF,因为图像中的平滑区域是否模糊,对图像质量影响不大,但是图像中的强边缘经过模糊后则有了较多的改变.因此对于如何将模糊图像的强边缘信息应用到运动模糊复原问题的研究具有重要意义.观测图像的强边缘信息(Px,Py)的计算公式为 uy,|uy| T,Py=0,|uy|≤T, 式中, ux, uy分别表示当前估计图像的x方向和y方向的偏导数, T为一个阈 值.然后,利用下述方法估计PSF: arg min h {∥gx h Px∥2+∥gy h P22y∥+α∥h∥}s.t.∑hi,j=1, hi,j≥0. i,j其中,(gx, gy)表示图像g的梯度.采用最速下降法来求解该问题即可得到PSF. 其次,利用得到的点扩散函数,应用前面的基于指导滤波的图像复原算法恢复清晰图像.此方法能保持边缘并抑制振铃效应以及消除噪声.本文对所提出的两种方法分别与其它算法做出了实验对比.实验结果表明,本文所提出的算法能够在有效地抑制噪声和振铃效应的同时,还能够更好的保持图像的边缘和纹理细节.因此,本文算法可以获得更高质量的复原图像.
[Abstract]:As one of the important branch and research hotspots in the field of image processing , the research of image restoration always has important theoretical significance and wide application value . In the problem of image restoration , the observed degraded image can be simplified as the sum of linear invariant convolution kernel and Gaussian white noise . The mathematical model can be written as : where u ( x , y ) , g ( x , y ) and n ( x , y ) represent the point spread function ( PSF ) which causes image degradation .

Image blind restoration has been one of the most difficult problems in image restoration . In view of the problem of image blind restoration , this paper introduces the theoretical basis and main algorithms in detail . This paper mainly focuses on the motion blur of the obtained image due to the relative position movement between the camera and the scene , and puts forward an effective image blind restoration algorithm , which mainly works as follows :

1 . An image blind restoration algorithm based on frequency domain iteration and guidance filtering is proposed .

First , the point spread function is estimated in the frequency domain . The frequency domain iteration formula is in which F denotes the Fourier transform operator , F ( . ) * denotes the complex conjugate of F , 伪 1 and 伪2 are constants . We estimate the approximate solution of the PSF using the frequency domain iterative method .

Second , the approximate solution of the estimated PSF is used as the initial value , and the problem of blind restoration of the image becomes a non - blind restoration problem . Since the guidance filtering can effectively remove the noise of the image and suppress the ringing effect on the premise of keeping the edge of the image not blurred , the original value of the target image is recovered by applying the restoration algorithm based on the guidance filtering .

the function expression for guiding the filtering is : wherein , u , and up represent the guiding image and the filtered image , respectively , u represents the filtered image , and omega is the size of the selection window , and epsilon 0 is the regularization parameter .

Consider the following two functions , u . is the pre - estimated image , 位0 is the regularization parameter . The solution u , and up are used as the guide image and the filtered input image , respectively , and the image up is smoothed by the guide filtering to achieve the purpose of de - noising , and then a clearer image is obtained .

finally , solving the two parts alternately , and obtaining the final clear image .

2 . An image blind restoration algorithm based on strong edge detection and guidance filtering is proposed .

Firstly , the PSF of the exit point spread function is estimated by using the strong edge information of the image , because the smooth region in the image is fuzzy , the influence on the image quality is not large , but the strong edge of the image is changed more after the blur . Therefore , it is important to apply the strong edge information of the blurred image to the research of motion blur restoration . The calculation formula of the strong edge information ( Px , py ) of the observation image is





uy , uuy = T , py = 0 , uuy = 鈮，

本文编号：1814247