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CN102682437A - Image deconvolution method based on total variation regularization - Google Patents

Image deconvolution method based on total variation regularization Download PDF

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CN102682437A
CN102682437A CN2012101547295A CN201210154729A CN102682437A CN 102682437 A CN102682437 A CN 102682437A CN 2012101547295 A CN2012101547295 A CN 2012101547295A CN 201210154729 A CN201210154729 A CN 201210154729A CN 102682437 A CN102682437 A CN 102682437A
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deconvolution
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谢立
胡玲玲
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Zhejiang University ZJU
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Abstract

本发明公开了一种基于总变分正则约束的图像解卷积方法。首先利用总变分(Total Variation TV)正则化Richardson-Lucy(RL)解卷积方法对图像进行解卷积，得到一副清晰图像作为参考图像ug；其次利用canny算子对参考图像进行边缘检测，得到图像平坦区和纹理区；接着，在纹理区应用标准Richardson-Lucy算法，在平坦区应用总变分正则约束的Richardson-Lucy算法，得到一幅比参考图像更清晰的图像uf；最后，对得到的图像进行双边滤波得到uB获得图像的细节层ud，最终将清晰图像uf加上细节层ud得到清晰图像u。仿真结果表明，本发明在振铃效应抑制和细节保存方面都优于标准RL算法和TV正则约束的RL算法。

Figure 201210154729

The invention discloses an image deconvolution method based on total variation regular constraints. First, use the Total Variation TV (Total Variation TV) regularized Richardson-Lucy (RL) deconvolution method to deconvolute the image to obtain a clear image as the reference image u g ; secondly, use the canny operator to edge the reference image Detect to obtain the flat area and texture area of the image; then, apply the standard Richardson-Lucy algorithm in the texture area, and apply the Richardson-Lucy algorithm constrained by total variation regularization in the flat area to obtain a clearer image u f than the reference image; Finally, perform bilateral filtering on the obtained image to obtain u B to obtain the image detail layer u d , and finally add the clear image u f to the detail layer u d to obtain the clear image u. The simulation results show that the present invention is superior to the standard RL algorithm and the RL algorithm constrained by TV regularity in terms of ringing effect suppression and detail preservation.

Figure 201210154729

Description

一种基于总变分正则约束的图像解卷积方法An Image Deconvolution Method Based on Total Variational Regularization Constraints

技术领域 technical field

本发明涉及图像处理，尤其涉及一种基于总变分正则约束的图像解卷积方法。The invention relates to image processing, in particular to an image deconvolution method based on total variation regular constraints.

背景技术 Background technique

随着现代成像技术的迅速发展，产生的图像数据在细节和体积上都是前所未有的，对这些图像数据的处理使得图像处理和计算机视觉的重要性愈发凸显。图像复原是图像处理中的一项重要内容，其主要目的是减轻或者消除图像采集或者传输过程中产生的品质退化现象，使得到的图像尽可能的逼近理想清晰图像，提高图像视觉效果，恢复图像中的各种信息。由于获取的图像在很多场景中并不能重现，比如视频监控获取的图像，某一时刻拍摄得到的天文图像，侦察照片等等，如果捕捉到的图像记录中有很重要的文字等标识信息可能会因为图像质量的退化而无法辨认，因此如何从模糊的、不真实的退化图像中复原得到逼真的清晰图像具有重要的现实意义。With the rapid development of modern imaging technology, the image data generated are unprecedented in detail and volume, and the processing of these image data makes image processing and computer vision more and more important. Image restoration is an important part of image processing. Its main purpose is to reduce or eliminate the quality degradation in the process of image acquisition or transmission, so that the obtained image is as close as possible to the ideal clear image, improve the visual effect of the image, and restore the image. various information in . Since the acquired images cannot be reproduced in many scenes, such as images acquired by video surveillance, astronomical images captured at a certain moment, reconnaissance photos, etc., if there are important text and other identification information in the captured image records, it may It will be unrecognizable due to the degradation of image quality, so how to restore a realistic and clear image from a blurred and unreal degraded image has important practical significance.

通常，我们将模糊图像表达为清晰图像与模糊核的卷积再加上噪声的形式，因此图像的复原转变为解卷积问题。根据模糊核是否已知，解卷积通常可以分为盲解卷积和非盲解卷积。近年来，出现了各种模糊图像解卷积的方法，非盲解卷积主要包括一些经典的方法如维纳滤波、卡尔曼滤波、约束最小二乘法、Richardson-Lucy（RL）算法等，其中近些年以RL算法应用最为广泛，但是RL随着迭代次数的增加会出现严重的振铃效应和噪声放大等问题。另外还有一些使用了图像的先验假设来约束求解过程，如稀疏先验、拉普拉斯先验、超拉普拉斯先验等。这些算法虽然可以较好的抑制振铃效应并减少噪声，但是得到的图像会过于平滑，部分图像细节丢失。盲解卷积方法因为模糊核未知变得更加复杂，通常都先进行模糊核的估计，然后使用非盲解卷积的方法进行图像去模糊。因此非盲解卷积在模糊图像盲复原过程中也有着重要的意义。Usually, we express the blurred image as the convolution of the clear image and the blur kernel plus noise, so the restoration of the image is transformed into a deconvolution problem. According to whether the blur kernel is known or not, deconvolution can generally be divided into blind deconvolution and non-blind deconvolution. In recent years, various fuzzy image deconvolution methods have emerged. Non-blind deconvolution mainly includes some classic methods such as Wiener filter, Kalman filter, constrained least squares method, Richardson-Lucy (RL) algorithm, etc., among which In recent years, the RL algorithm is the most widely used, but RL will have serious problems such as ringing effect and noise amplification as the number of iterations increases. There are also some prior assumptions that use the image to constrain the solution process, such as sparse prior, Laplacian prior, super Laplacian prior, etc. Although these algorithms can better suppress the ringing effect and reduce noise, the resulting image will be too smooth and some image details will be lost. The blind deconvolution method becomes more complicated because the blur kernel is unknown. Usually, the blur kernel is estimated first, and then the non-blind deconvolution method is used to deblur the image. Therefore, non-blind deconvolution is also of great significance in the process of blind restoration of blurred images.

发明内容 Contents of the invention

本发明的目的在于提供一种基于总变分正则约束的图像解卷积方法。The purpose of the present invention is to provide an image deconvolution method based on total variation regular constraints.

为实现上述目的，本发明采用的技术方案是：In order to achieve the above object, the technical scheme adopted in the present invention is:

基于总变分正则约束的图像解卷积方法包括如下步骤：The image deconvolution method based on the total variation regular constraint includes the following steps:

1）由于图像采集过程中的相机抖动引起的图像运动模糊通常表达为清晰图像与模糊核的卷积再加上噪声的形式，1) Image motion blur caused by camera shake during image acquisition is usually expressed as the convolution of clear image and blur kernel plus noise,

gg == KK ⊗⊗ uu ++ NN -- -- -- (( 11 ))

式（1）中，g表示模糊图像，K模糊核，u表示未模糊清晰图像，N表示噪声，

Figure BDA00001652056800012
表示卷积操作，其中g和K已知，且假定模糊核具有空间移不变性，即模糊图像的全图受到同一个模糊核函数的影响，解卷积的目的就是利用已知的模糊图像和模糊核得到清晰图像u；In formula (1), g represents the blurred image, K represents the blur kernel, u represents the unblurred clear image, N represents the noise,
Figure BDA00001652056800012
Represents a convolution operation, where g and K are known, and it is assumed that the blur kernel has spatial shift invariance, that is, the entire image of the blurred image is affected by the same blur kernel function, and the purpose of deconvolution is to use the known blurred image and The blur kernel obtains a clear image u;

2）利用总变分约束Richardson-Lucy算法解卷积过程得到一个参考图像，参考图像相对于利用标准Richardson-Lucy解卷积得到的图像平滑，但是图像解卷积过程中易出现的振铃效应和噪声放大得到了好的抑制，2) Using the deconvolution process of the total variation constraint Richardson-Lucy algorithm to obtain a reference image, the reference image is smoother than the image obtained by standard Richardson-Lucy deconvolution, but the ringing effect that is prone to appear in the image deconvolution process and noise amplification are well suppressed,

总变分约束正则项形式为：The form of the total variation constraint regular term is:

RR TVTV (( uu )) == ∫∫ || || ▿▿ uu (( xx )) || || 22 dxdx -- -- -- (( 22 ))

其中

Figure BDA00001652056800014
是清晰图像u(x)的一阶导数；in
Figure BDA00001652056800014
is the first derivative of the clear image u(x);

得到图像解卷积的迭代更新公式为：The iterative update formula for image deconvolution is:

uu tt ++ 11 == uu tt 11 -- λλ ▿▿ RR TVTV (( uu tt )) ×× KK ** ⊗⊗ gg uu tt ⊗⊗ KK -- -- -- (( 33 ))

其中，

Figure BDA00001652056800022
λ为控制正则项权重的参数，取值范围为[0,1]，对图像进行解卷积得到参考图像ug，对参考图像ug进行canny边缘检测，然后做形态学膨胀，得到图像的平坦区和纹理区掩膜M；in,
Figure BDA00001652056800022
λ is a parameter to control the weight of the regularization term, and the value range is [0,1]. Deconvolute the image to obtain the reference image u g , perform canny edge detection on the reference image u g , and then perform morphological expansion to obtain the image flat area and texture area mask M;

3）在平坦区用总变分正则约束解卷积过程，而在纹理区使用标准Richardson-Lucy算法进行更新迭代，整个过程的迭代更新公式为：3) The deconvolution process is constrained by the total variational regularization in the flat area, and the standard Richardson-Lucy algorithm is used for update iterations in the texture area. The iterative update formula of the whole process is:

Figure BDA00001652056800023
Figure BDA00001652056800023

其中，在平坦区像素对应的M值为1，纹理区像素对应的M值为0，Among them, the M value corresponding to the pixel in the flat area is 1, and the M value corresponding to the pixel in the texture area is 0,

按式（4）解卷积得到清晰图像uf，使用双边滤波器对清晰图像uf进行滤波得到滤波后的图像uB；Deconvolve according to formula (4) to obtain a clear image u f , and use a bilateral filter to filter the clear image u f to obtain a filtered image u B ;

4）对滤波后的图像uB再次进行双边滤波得到图像F(uB)，并将图像F(uB)与滤波后的图像uB进行作差，得到抑制噪声的图像细节层ud，4) Perform bilateral filtering on the filtered image u B again to obtain the image F(u B ), and make a difference between the image F(u B ) and the filtered image u B to obtain the noise-suppressed image detail layer u d ,

ud＝uB-F(uB)           （5）u d ＝u B -F(u B ) (5)

进一步的对清晰图像uf做如下操作得到最终清晰图像u：Further perform the following operations on the clear image u f to obtain the final clear image u:

u＝uf+ud               （6）。u = u f + u d (6).

本发明与现有技术相比具有的有益效果：The present invention has the beneficial effect compared with prior art:

1）本发明结合了标准Richardson-Lucy和总变分正则化约束的优缺点设计了一种图像去模糊问题中解卷积的新算法。不仅可以有效的抑制图像去模糊问题中极易出现的振铃效应和噪声放大问题，同时可以恢复原始图像中被破坏的细节信息。且本解卷积方法只需要单张模糊图像作为输入便可以得到令人满意的视觉效果，大大满足了人们日常生活和科研活动的应用要求。1) The present invention combines the advantages and disadvantages of the standard Richardson-Lucy and total variational regularization constraints to design a new algorithm for deconvolution in the image deblurring problem. Not only can it effectively suppress the ringing effect and noise amplification problems that are very easy to appear in the image deblurring problem, but it can also restore the damaged details in the original image. Moreover, the deconvolution method only needs a single fuzzy image as an input to obtain a satisfactory visual effect, which greatly meets the application requirements of people's daily life and scientific research activities.

2）由于模糊图像中图像的纹理特征并不明显，本方法利用总变分正则约束解卷积得到的图像来判断纹理区和平坦区的大大增加了算法的准确性。2) Since the texture features of the image in the blurred image are not obvious, this method uses the image obtained by the deconvolution of the total variational regularization constraint to judge the texture area and the flat area, which greatly increases the accuracy of the algorithm.

附图说明 Description of drawings

图1是基于总变分正则约束的图像非盲解卷积方法的流程示意图；Figure 1 is a schematic flow diagram of an image non-blind deconvolution method based on total variation regular constraints;

图2是本发明使用的原始清晰图像；Fig. 2 is the original clear image used by the present invention;

图3是本发明使用模糊图像对应的模糊核；Fig. 3 is the fuzzy kernel corresponding to the blurred image used in the present invention;

图4是本发明使用的清晰图像对应的模糊图像；Fig. 4 is the fuzzy image corresponding to the clear image used in the present invention;

图5是利用标准Richardson-Lucy算法的获得的清晰图像；Figure 5 is a clear image obtained using the standard Richardson-Lucy algorithm;

图6是利用总变分约束获得的清晰图像；Figure 6 is a clear image obtained using the total variation constraint;

图7是本发明获得的清晰图像；Fig. 7 is the clear image that the present invention obtains;

图8是图4到图7对应的局部放大图对比图。Fig. 8 is a comparison diagram of partial enlarged diagrams corresponding to Fig. 4 to Fig. 7 .

具体实施方式 Detailed ways

基于总变分正则约束的图像解卷积方法包括如下步骤：The image deconvolution method based on the total variation regular constraint includes the following steps:

1）由于图像采集过程中的相机抖动引起的图像运动模糊通常表达为清晰图像与模糊核的卷积再加上噪声的形式，1) Image motion blur caused by camera shake during image acquisition is usually expressed as the convolution of clear image and blur kernel plus noise,

gg == KK ⊗⊗ uu ++ NN -- -- -- (( 11 ))

式（1）中，g表示模糊图像，K模糊核，u表示未模糊清晰图像，N表示噪声，

Figure BDA00001652056800032
表示卷积操作，其中g和K已知，且假定模糊核具有空间移不变性，即模糊图像的全图受到同一个模糊核函数的影响，解卷积的目的就是利用已知的模糊图像和模糊核得到清晰图像u；In formula (1), g represents the blurred image, K represents the blur kernel, u represents the unblurred clear image, N represents the noise,
Figure BDA00001652056800032
Represents a convolution operation, where g and K are known, and it is assumed that the blur kernel has spatial shift invariance, that is, the entire image of the blurred image is affected by the same blur kernel function, and the purpose of deconvolution is to use the known blurred image and The blur kernel obtains a clear image u;

2）利用总变分约束Richardson-Lucy算法解卷积过程得到一个参考图像，参考图像相对于利用标准Richardson-Lucy解卷积得到的图像平滑，但是图像解卷积过程中易出现的振铃效应和噪声放大得到了好的抑制，2) Using the deconvolution process of the total variation constraint Richardson-Lucy algorithm to obtain a reference image, the reference image is smoother than the image obtained by standard Richardson-Lucy deconvolution, but the ringing effect that is prone to appear in the image deconvolution process and noise amplification are well suppressed,

总变分约束正则项形式为：The form of the total variation constraint regular term is:

RR TVTV (( uu )) == ∫∫ || || ▿▿ uu (( xx )) || || 22 dxdx -- -- -- (( 22 ))

其中

Figure BDA00001652056800034
是清晰图像u(x)的一阶导数；in
Figure BDA00001652056800034
is the first derivative of the clear image u(x);

得到图像解卷积的迭代更新公式为：The iterative update formula for image deconvolution is:

uu tt ++ 11 == uu tt 11 -- λλ ▿▿ RR TVTV (( uu tt )) ×× KK ** ⊗⊗ gg uu tt ⊗⊗ KK -- -- -- (( 33 ))

其中，

Figure BDA00001652056800036
λ为控制正则项权重的参数，取值范围为[0,1]，对图像进行解卷积得到参考图像ug，对参考图像ug进行canny边缘检测，然后做形态学膨胀，得到图像的平坦区和纹理区掩膜M；in,
Figure BDA00001652056800036
λ is a parameter to control the weight of the regularization term, and the value range is [0,1]. Deconvolute the image to obtain the reference image u g , perform canny edge detection on the reference image u g , and then perform morphological expansion to obtain the image flat area and texture area mask M;

3）在平坦区用总变分正则约束解卷积过程，而在纹理区使用标准Richardson-Lucy算法进行更新迭代，整个过程的迭代更新公式为：3) The deconvolution process is constrained by the total variational regularization in the flat area, and the standard Richardson-Lucy algorithm is used for update iterations in the texture area. The iterative update formula of the whole process is:

Figure BDA00001652056800037
Figure BDA00001652056800037

其中，在平坦区像素对应的M值为1，纹理区像素对应的M值为0，Among them, the M value corresponding to the pixel in the flat area is 1, and the M value corresponding to the pixel in the texture area is 0,

按式（4）解卷积得到清晰图像uf，使用双边滤波器对清晰图像uf进行滤波得到滤波后的图像uB；Deconvolve according to formula (4) to obtain a clear image u f , and use a bilateral filter to filter the clear image u f to obtain a filtered image u B ;

4）对滤波后的图像uB再次进行双边滤波得到图像F(uB)，并将图像F(uB)与滤波后的图像uB进行作差，得到抑制噪声的图像细节层ud，4) Perform bilateral filtering on the filtered image u B again to obtain the image F(u B ), and make a difference between the image F(u B ) and the filtered image u B to obtain the noise-suppressed image detail layer u d ,

ud＝uB-F(uB)      （5）u d ＝u B -F(u B ) (5)

进一步的对清晰图像uf做如下操作得到最终清晰图像u：Further perform the following operations on the clear image u f to obtain the final clear image u:

u＝uf+ud          （6）。u = u f + u d (6).

实施例Example

本发明的最终目的是从一幅模糊图像中利用已知的模糊核函数解卷积得到一幅清晰图像。为了更好的理解本发明的技术方案，以下举例说明本发明整个过程的具体实施方式如下：The ultimate purpose of the present invention is to obtain a clear image from a blurred image by deconvolution using a known blur kernel function. In order to better understand the technical scheme of the present invention, the specific implementation manner of the whole process of the present invention is illustrated below as follows:

1）由于图像采集过程中的相机抖动等引起的图像运动模糊通常表达为清晰图像与模糊核的卷积再加上噪声的形式，1) Image motion blur caused by camera shake during image acquisition is usually expressed as the convolution of clear image and blur kernel plus noise,

gg == KK ⊗⊗ uu ++ NN -- -- -- (( 11 ))

本发明中g和K已知，且假定模糊核具有空间移不变性，即模糊图像的全图受到同一个模糊核函数的影响，图像去模糊的目的就是从模糊图像中复原得到清晰图像，由于模糊图像和模糊核已知，图像去模糊问题就简化为图像解卷积问题；In the present invention, g and K are known, and it is assumed that the blur kernel has spatial shift invariance, that is, the whole picture of the blurred image is affected by the same blur kernel function, and the purpose of image deblurring is to restore a clear image from the blurred image, because The blurred image and blur kernel are known, and the image deblurring problem is simplified to the image deconvolution problem;

2）利用总变分约束RL算法解卷积过程得到一个参考图像，此参考图像相对于利用标准Richardson-Lucy解卷积得到的图像较平滑，但是图像解卷积过程中易出现的振铃效应和噪声放大得到了较好的抑制，2) Use the total variation constrained RL algorithm deconvolution process to obtain a reference image, which is smoother than the image obtained by standard Richardson-Lucy deconvolution, but the ringing effect that is prone to appear in the image deconvolution process and noise amplification are better suppressed,

总变分约束正则项形式为：The form of the total variation constraint regular term is:

RR TVTV (( uu )) == ∫∫ || || ▿▿ uu (( xx )) || || 22 dxdx -- -- -- (( 22 ))

总变分约束正则化图像解卷积的迭代更新公式为：The iterative update formula for total variation constrained regularized image deconvolution is:

uu tt ++ 11 == uu tt 11 -- λλ ▿▿ RR TVTV (( uu tt )) ×× KK ** ⊗⊗ gg uu tt ⊗⊗ KK -- -- -- (( 33 ))

根据式（3）迭代更新公式，将λ取为0.51，利用总变分约束正则化图像解卷积方法对图像进行解卷积得到参考图像ug，见附图6，According to formula (3) iterative update formula, λ is taken as 0.51, and the reference image u g is obtained by deconvolving the image using the total variation constraint regularized image deconvolution method, as shown in Figure 6,

对参考图像ug进行canny边缘检测，边缘检测的上下阈值分别为0.05和0.09，然后采用边长为5个像素大小的正方形结构元素做形态学膨胀，得到图像的平坦区和纹理区掩膜M；Carry out canny edge detection on the reference image u g , the upper and lower thresholds of edge detection are 0.05 and 0.09 respectively, and then use square structural elements with a side length of 5 pixels for morphological expansion to obtain the flat area and texture area mask M of the image ;

3）结合总变分正则化解卷积和标准Richardson-Lucy解卷积方法的优缺点，在平坦区用TV正则约束解卷积过程，而在纹理区使用标准Richardson-Lucy算法进行更新迭代，整个过程的迭代更新公式为：3) Combining the advantages and disadvantages of the total variation regularized deconvolution and the standard Richardson-Lucy deconvolution method, the TV regularization is used to constrain the deconvolution process in the flat area, and the standard Richardson-Lucy algorithm is used for update iterations in the texture area. The iterative update formula of the process is:

Figure BDA00001652056800044
Figure BDA00001652056800044

按式（4）解卷积得到清晰图像uf，使用双边滤波器对清晰图像uf进行滤波得到滤波后的图像uB，Deconvolve according to formula (4) to obtain a clear image u f , use a bilateral filter to filter the clear image u f to obtain a filtered image u B ,

双边滤波器的算法为：The algorithm of bilateral filter is:

Ff (( II (( xx )) )) == 11 ZZ xx ΣΣ ythe y ∈∈ WW ff (( || xx -- ythe y || )) gg (( || II (( xx )) -- II (( ythe y )) || )) II (( ythe y )) -- -- -- (( 55 ))

其中，I为待滤波图像，F(I(x))为双边滤波后的图像，Zx为归一化项，W为图像像素空间，x和y均为图像中像素点的坐标，f和g分别为空间域影响函数和灰度域影响函数，一般使用高斯函数来描述。即有：Among them, I is the image to be filtered, F(I(x)) is the image after bilateral filtering, Z x is the normalization item, W is the image pixel space, x and y are the coordinates of the pixel points in the image, f and g is the spatial domain influence function and the gray domain influence function, which are generally described by Gaussian functions. That is:

ff (( || xx -- ythe y || )) == expexp (( -- || xx -- ythe y || 22 22 σσ sthe s )) -- -- -- (( 66 ))

gg (( || II (( xx )) -- II (( ythe y )) || )) == expexp (( -- || II (( xx )) -- II (( ythe y )) || 22 22 σσ rr )) -- -- -- (( 77 ))

本方法中，σs和σr的值分别取3和0.1；In this method, the values of σs and σr are 3 and 0.1 respectively;

4）由于此时获得的清晰图像uf通常含有噪声，如果直接将清晰图像与双边滤波后的图像作差得到图像细节层相加得到增加细节的图像会放大噪声，为了抑制噪声，对双边滤波后的图像uB再次进行双边滤波得到图像F(uB)，并将图像F(uB)与第一次双边滤波后的图像uB进行作差，得到抑制噪声的图像细节层ud，即：4) Since the clear image u f obtained at this time usually contains noise, if the difference between the clear image and the bilaterally filtered image is directly obtained by adding the image detail layer to obtain an image with increased details, the noise will be amplified. In order to suppress the noise, the bilateral filter After the image u B is subjected to bilateral filtering again to obtain the image F(u B ), and the difference between the image F(u B ) and the image u B after the first bilateral filtering is obtained to obtain the noise-suppressed image detail layer u d , Right now:

ud＝uB-F(uB)            （8）u d ＝u B -F(u B ) (8)

进一步的对清晰图像做如下操作得到最终清晰图像u，：Further perform the following operations on the clear image to obtain the final clear image u,:

u＝uf+ud                （9）u = u f + u d (9)

清晰图像u见附图7。The clear image u is shown in Figure 7.

Claims (1)

1.一种基于总变分正则约束的图像解卷积方法，其特征是包括如下步骤：1. a kind of image deconvolution method based on total variation regular constraint, it is characterized in that comprising the steps: 1）由于图像采集过程中的相机抖动引起的图像运动模糊通常表达为清晰图像与模糊核的卷积再加上噪声的形式，1) Image motion blur caused by camera shake during image acquisition is usually expressed as the convolution of clear image and blur kernel plus noise, gg == KK ⊗⊗ uu ++ NN -- -- -- (( 11 )) 式（1）中，g表示模糊图像，K模糊核，u表示未模糊清晰图像，N表示噪声，
Figure FDA00001652056700012
表示卷积操作，其中g和K已知，且假定模糊核具有空间移不变性，即模糊图像的全图受到同一个模糊核函数的影响，解卷积的目的就是利用已知的模糊图像和模糊核得到清晰图像u；In formula (1), g represents the blurred image, K represents the blur kernel, u represents the unblurred clear image, N represents the noise,
Figure FDA00001652056700012
Represents a convolution operation, where g and K are known, and it is assumed that the blur kernel has spatial shift invariance, that is, the entire image of the blurred image is affected by the same blur kernel function, and the purpose of deconvolution is to use the known blurred image and The blur kernel obtains a clear image u; 2）利用总变分约束Richardson-Lucy算法解卷积过程得到一个参考图像，参考图像相对于利用标准Richardson-Lucy解卷积得到的图像平滑，但是图像解卷积过程中易出现的振铃效应和噪声放大得到了好的抑制，2) Using the deconvolution process of the total variation constraint Richardson-Lucy algorithm to obtain a reference image, the reference image is smoother than the image obtained by standard Richardson-Lucy deconvolution, but the ringing effect that is prone to appear in the image deconvolution process and noise amplification are well suppressed, 总变分约束正则项形式为：The form of the total variation constraint regular term is: RR TVTV (( uu )) == ∫∫ || || ▿▿ uu (( xx )) || || 22 dxdx -- -- -- (( 22 )) 其中
Figure FDA00001652056700014
是清晰图像u(x)的一阶导数；in
Figure FDA00001652056700014
is the first derivative of the clear image u(x); 得到图像解卷积的迭代更新公式为：The iterative update formula for image deconvolution is: uu tt ++ 11 == uu tt 11 -- λλ ▿▿ RR TVTV (( uu tt )) ×× KK ** ⊗⊗ gg uu tt ⊗⊗ KK -- -- -- (( 33 )) 其中，λ为控制正则项权重的参数，取值范围为[0,1]，对图像进行解卷积得到参考图像ug，对参考图像ug进行canny边缘检测，然后做形态学膨胀，得到图像的平坦区和纹理区掩膜M；in, λ is a parameter to control the weight of the regularization term, and the value range is [0,1]. Deconvolute the image to obtain the reference image u g , perform canny edge detection on the reference image u g , and then perform morphological expansion to obtain the image flat area and texture area mask M; 3）在平坦区用总变分正则约束解卷积过程，而在纹理区使用标准Richardson-Lucy算法进行更新迭代，整个过程的迭代更新公式为：3) The deconvolution process is constrained by the total variational regularization in the flat area, and the standard Richardson-Lucy algorithm is used for update iterations in the texture area. The iterative update formula of the whole process is: 其中，在平坦区像素对应的M值为1，纹理区像素对应的M值为0，Among them, the M value corresponding to the pixel in the flat area is 1, and the M value corresponding to the pixel in the texture area is 0, 按式（4）解卷积得到清晰图像uf，使用双边滤波器对清晰图像uf进行滤波得到滤波后的图像uB；Deconvolve according to formula (4) to obtain a clear image u f , and use a bilateral filter to filter the clear image u f to obtain a filtered image u B ; 4）对滤波后的图像uB再次进行双边滤波得到图像F(uB)，并将图像F(uB)与滤波后的图像uB进行作差，得到抑制噪声的图像细节层ud，4) Perform bilateral filtering on the filtered image u B again to obtain the image F(u B ), and make a difference between the image F(u B ) and the filtered image u B to obtain the noise-suppressed image detail layer u d , ud＝uB-F(uB)           （5）u d ＝u B -F(u B ) (5) 进一步的对清晰图像uf做如下操作得到最终清晰图像uu：Further perform the following operations on the clear image u f to obtain the final clear image u u : u＝uf+ud               （6）。u = u f + u d (6).
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