本文選題：圖像盲復(fù)原 + 點(diǎn)擴(kuò)散函數(shù)��； 參考：《吉林大學(xué)》2015年博士論文

【摘要】：作為圖像處理領(lǐng)域的重要分支和研究熱點(diǎn)之一,圖像復(fù)原方法的研究始終具有重要理論意義和廣泛的應(yīng)用價(jià)值.在圖像復(fù)原問(wèn)題中,觀測(cè)的退化圖像通常可以簡(jiǎn)化為線性移不變卷積核與高斯白噪聲之和,其數(shù)學(xué)模型可以寫成：其中,u(x,y),g(x,y)和n(x,y)分別表示原始圖像,退化圖像和加性噪聲,h(x,y)表示引起圖像退化的點(diǎn)擴(kuò)散函數(shù)(PSF),”*”表示卷積算子.大多數(shù)復(fù)原算法都是建立在點(diǎn)擴(kuò)散函數(shù)已知的前提下,而在實(shí)際問(wèn)題中,點(diǎn)擴(kuò)散函數(shù)通常是未知的.因此對(duì)盲復(fù)原理論及算法的研究,有著理論意義與實(shí)際需求. 圖像盲復(fù)原一直以來(lái)都是圖像復(fù)原中比較困難的問(wèn)題之一.針對(duì)圖像盲復(fù)原問(wèn)題,本文詳細(xì)地介紹了其理論基礎(chǔ)和主要算法.本文主要針對(duì)相機(jī)與所拍攝景物之間由于相對(duì)位置移動(dòng)而使所獲得圖像發(fā)生運(yùn)動(dòng)模糊的情況,提出了有效的圖像盲復(fù)原算法,主要工作如下： 1.提出了一種基于頻域迭代和指導(dǎo)濾波的圖像盲復(fù)原算法. 首先,在頻域上估計(jì)點(diǎn)擴(kuò)散函數(shù).頻域迭代公式為其中,F表示Fourier變換算子,F(.)*表示F的復(fù)共軛,α1和α2為常數(shù).我們利用頻域迭代法估計(jì)出PSF的近似解. 其次,將估計(jì)出的PSF的近似解作為初始值,此時(shí)圖像盲復(fù)原問(wèn)題變成了非盲復(fù)原問(wèn)題.由于指導(dǎo)濾波能夠在保持圖像邊緣不被模糊的前提下,有效地去除圖像的噪聲并抑制振鈴效應(yīng).因此,應(yīng)用基于指導(dǎo)濾波的復(fù)原算法恢復(fù)出目標(biāo)圖像初值. 指導(dǎo)濾波的函數(shù)表達(dá)式為：其中,u,和up分別表示指導(dǎo)圖像和濾波圖像,u表示濾波后的圖像,ω是選擇窗口的大小,ε0是正則化參數(shù). 考慮下面兩個(gè)函數(shù)其中,u。是預(yù)估計(jì)圖像,λ0是正則化參數(shù).將其解u,和up分別作為指導(dǎo)圖像和濾波輸入圖像,利用指導(dǎo)濾波對(duì)圖像up進(jìn)行平滑以達(dá)到去噪的目的,進(jìn)而得到更清晰的圖像. 最后,將上述兩部分交替迭代求解,可以得到最終的清晰圖像. 2.提出了基于強(qiáng)邊緣檢測(cè)和指導(dǎo)濾波的圖像盲復(fù)原算法. 首先,利用圖像的強(qiáng)邊緣信息來(lái)估計(jì)出點(diǎn)擴(kuò)散函數(shù)PSF,因?yàn)閳D像中的平滑區(qū)域是否模糊,對(duì)圖像質(zhì)量影響不大,但是圖像中的強(qiáng)邊緣經(jīng)過(guò)模糊后則有了較多的改變.因此對(duì)于如何將模糊圖像的強(qiáng)邊緣信息應(yīng)用到運(yùn)動(dòng)模糊復(fù)原問(wèn)題的研究具有重要意義.觀測(cè)圖像的強(qiáng)邊緣信息(Px,Py)的計(jì)算公式為 uy,|uy| T,Py=0,|uy|≤T, 式中, ux, uy分別表示當(dāng)前估計(jì)圖像的x方向和y方向的偏導(dǎo)數(shù), T為一個(gè)閾 值.然后,利用下述方法估計(jì)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)表示圖像g的梯度.采用最速下降法來(lái)求解該問(wèn)題即可得到PSF. 其次,利用得到的點(diǎn)擴(kuò)散函數(shù),應(yīng)用前面的基于指導(dǎo)濾波的圖像復(fù)原算法恢復(fù)清晰圖像.此方法能保持邊緣并抑制振鈴效應(yīng)以及消除噪聲.本文對(duì)所提出的兩種方法分別與其它算法做出了實(shí)驗(yàn)對(duì)比.實(shí)驗(yàn)結(jié)果表明,本文所提出的算法能夠在有效地抑制噪聲和振鈴效應(yīng)的同時(shí),還能夠更好的保持圖像的邊緣和紋理細(xì)節(jié).因此,本文算法可以獲得更高質(zhì)量的復(fù)原圖像.
[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 , 偽 1 and 偽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，

本文編號(hào)：1814247