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摘要:
非盲图像复原在数学上是一种典型的病态问题，也是计算机视觉领域的重要研究内容之一，其目标是在点扩散函数已知的情况下，由模糊图像估计出清晰图像，其研究重点是在改善图像清晰度和抑制噪声之间做出适当的折衷。 近50年来，非盲图像复原取得了长足的发展，从早期的维纳滤波到当前的深度学习，学者们提出了数以百计的非盲图像复原算法，并应用在各个领域。本文首先介绍非盲图像复原的基本概念和研究意义，然后依据算法的属性对非盲图像复原算法进行分类概括，从总体上将其分为传统方法和深度学习方法，又进一步将传统方法细分为直接法和迭代法，并依据不同算法的模型特征，分析不同类别中主要算法的优缺点，同时结合多种典型实验，比较分析了一些代表性算法的复原性能，最后展望了非盲图像复原算法的发展趋势，归纳了重点研究方向。
Abstract:Non-blind image restoration is one of the most improtant research topics in the field of computer vision. It is also a typical ill-posed problem in mathematics. Its goal is to estimate a clear image from a blurred image when the point spread function is known. Its research focuses on how to make an appropriate compromise between improving clarity and suppressing noise. In the past 50 years, non-blind image restoration has made great progress. From the Wiener filtering to deep learning based methods, scholars have proposed hundreds of non-blind image restoration algorithms and applied them in various academic fields. This paper first introduces the basic concept and research significance of non-blind image restoration, then classifies and summarizes the main non-blind image restoration algorithms according to the algorithm attributes, which are generally divided into traditional methods and deep learning based methods. The traditional methods are divided into the direct method and iterative method, then are analyzed for their advantages and disadvantages. The performance of representative restoration algorithms is compared in a varity of typical experiments. Finally, the development trend and important research directions of non-blind image restoration algorithms are proposed.
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Key words:
- non blind image restoration /
- image priors /
- direct method /
- iterative scheme /
- deep learning
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表 1 实验设置
Table 1. Experimental settings
序号 点扩散函数 噪声水平 图像 1 9 × 9 boxcar BSNR = 40 dB Cameraman 2 $k(x,y) = 1/({x^2} + {y^2}),x,y = - 7,\cdots,7$ $ {\sigma ^2} = 2 $ Cameraman 3 $k(x,y) = 1/({x^2} + {y^2}),x,y = - 7,\cdots,7$ $ {\sigma ^2} = 8 $ Cameraman 4 $k = {[1,4,6,4,1]^{\rm{T}}}[1,4,6,4,1]/256$ $ {\sigma ^2} = 49 $ Lena 5 Gaussian型点扩散函数，方差为1.6 $ {\sigma ^2} = 2 $ Barbara 6 Gaussian型点扩散函数，方差为0.4 $ {\sigma ^2} = 64 $ House 
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表 3 迭代法实验设置
Table 3. Experimental setup for iterative methods
序号 点扩散函数 噪声水平 1 $ k(x,y) = 1/({x^2} + {y^2}),x,y = - 7,\cdots,7 $ ${\sigma ^2} = 2$ 2 $ k(x,y) = 1/({x^2} + {y^2}),x,y = - 7,\cdots,7 $ ${\sigma ^2} = 8 $ 3 9 × 9 boxcar BSNR = 40 dB 4 $ k = {[1,4,6,4,1]^{\rm{T} } }[1,4,6,4,1]/256 $ ${\sigma ^2} = 49 $ 5 Gaussian型点扩散函数，方差为1.6 ${\sigma ^2} = 2 $ 6 Gaussian型点扩散函数，方差为0.4 ${\sigma ^2} = 64 $
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表 4 迭代法实验对比 ISNR
Table 4. Experimental comparison of ISNR
(单位:dB) 实验序号 1 2 3 4 5 6 方法 Cameraman BM3DDEB[31] 8.19 6.40 8.34 3.34 3.73 4.70 L0-Abs[62] 7.70 5.55 9.10 2.93 3.49 1.77 CGMK[36] 7.80 5.49 9.15 2.80 3.54 3.33 TVMM[34] 7.41 5.17 8.54 2.57 3.36 1.30 GFD[33] 8.38 6.52 9.73 3.57 4.02 - NCSR[70] 8.78 6.69 10.33 3.78 4.60 4.50 GSR[71] 8.39 6.39 10.08 3.33 3.94 4.76 IDDBM3D[73] 8.85 7.12 10.45 3.98 4.31 4.89 LRD[76] 8.90 7.05 10.70 3.99 4.62 4.62 House BM3DDEB[31] 9.32 8.14 10.85 5.13 4.56 7.21 L0-Abs[62] 8.40 7.12 11.06 4.55 4.80 2.15 CGMK[36] 8.31 6.97 10.75 4.48 4.97 4.59 TVMM[34] 7.98 6.57 10.39 4.12 4.54 2.44 GFD[33] 9.39 7.75 12.02 5.21 5.39 NCSR[70] 9.96 8.48 13.12 5.81 5.67 6.94 GSR[71] 10.02 8.56 13.44 6.00 5.95 7.18 IDDBM3D[73] 9.95 8.55 12.89 5.79 5.74 7.13 LRD[76] 10.09 8.67 13.49 6.03 6.22 6.74 Lena BM3DDEB[31] 7.95 6.53 7.97 4.81 4.37 6.40 L0-Abs[62] 6.66 5.71 7.79 4.09 4.22 1.93 CGMK[36] 6.76 5.37 7.86 3.49 3.93 4.46 TVMM[34] 6.36 4.98 7.47 3.52 3.61 2.79 GFD[33] 8.12 6.65 8.97 4.77 4.95 - NCSR[70] 8.03 6.54 9.25 4.93 4.86 6.19 GSR[71] 8.24 6.76 9.43 5.17 4.96 6.57 IDDBM3D[73] 7.97 6.61 8.91 4.97 4.85 6.34 LRD[76] 8.25 6.78 9.31 5.13 5.08 6.13 Barbara BM3DDEB[31] 7.80 3.94 5.86 1.90 1.28 5.80 L0-Abs[62] 3.51 1.53 3.98 0.73 0.81 1.17 CGMK[36] 2.45 1.34 3.55 0.44 0.81 0.38 TVMM[34] 3.10 1.33 3.49 0.41 0.75 0.59 NCSR 7.76 3.64 5.92 2.06 1.43 5.50 GSR[71] 8.98 4.80 7.15 2.19 1.58 6.20 IDDBM3D[73] 7.64 3.96 6.05 1.88 1.16 5.45 LRD[76] 8.31 5.17 6.95 2.34 1.70 5.37
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表 5 深度学习方法的实验对比
Table 5. Experimental comparison of deep learning of different methods
Levin[106] Sun[107] Martin[108] σ 1% 3% 5% 1% 5% 1% 5% EPLL[82] 34.06 29.09 26.54 32.48 26.78 29.81 24.66 0.9310 0.8460 0.7785 0.8815 0.6975 0.8383 0.6276 CSF[84] 31.09 28.01 26.32 31.52 26.62 29.00 24.93 0.9024 0.8013 0.7427 0.8622 0.6735 0.8230 0.6428 MLP[89] 32.08 27.00 25.38 31.47 24.65 28.47 24.01 0.8884 0.7016 0.6330 0.8535 0.5198 0.7977 0.5619 LDT[109] 31.53 28.39 26.70 30.52 26.71 28.20 24.90 0.8977 0.8052 0.7468 0.8399 0.6694 0.7922 0.6358 FCN[94] 33.22 29.49 27.72 32.36 27.67 29.51 25.45 0.9267 0.8599 0.8142 0.8853 0.7340 0.8339 0.6771 IRCNN[93] 34.33 30.04 28.51 33.57 27.64 30.63 25.65 0.9210 0.8156 0.7762 0.8977 0.6884 0.8645 0.6640 FDN[87] 34.05 29.77 27.94 32.63 27.75 29.93 25.93 0.9335 0.8583 0.8139 0.8887 0.7319 0.8555 0.6943 FNBD[88] 34.81 30.63 27.93 31.22 27.63 30.92 25.49 0.9398 0.8658 0.7759 0.8860 0.7010 0.8799 0.6589 RGDN[92] 33.96 29.71 27.45 31.25 26.93 29.51 25.33 0.9395 0.8662 0.7889 0.8869 0.7161 0.8616 0.6688 VEM[99] 34.31 30.50 28.52 32.73 29.41 − − 0.9382 0.8798 0.8348 0.8952 0.8055 − − DWDN[101] 36.90 32.77 30.77 34.05 − 31.74 − 0.9614 0.9179 0.8857 0.9225 − 0.8938 − CV-CNN[97] 35.44 30.85 28.80 33.10 29.54 − − 0.9467 0.8829 0.8381 0.9022 0.8094 − − SVMAP[110] − − − 34.51 29.20 31.89 27.25 − − − 0.9273 0.7940 0.8973 0.7550
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