基于稀疏表示的单幅彩色图像超分辨率重建方法研究
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摘要
图像超分辨率重建的目的是根据单幅或者多幅低分辨率图像,采用信号处理技术,重建出高分辨率图像,其可分为单幅图像超分辨率重建和多幅图像超分辨率重建,本文主要研究单幅图像超分辨率重建。基于稀疏表示的超分辨率重建技术是当前图像处理领域研究的热点之一,其关键技术包括稀疏矩阵的计算、词典构建以及相关后处理技术。本文在分析词典构建算法以及训练样本集对重建质量影响分析的基础上,提出了改进的基于稀疏表示的彩色图像超分辨率重建方法,并对图像后处理技术进行了研究。主要工作包括：
1)词典构建算法性能验证。实现了两种典型的词典构建算法,并进行了性能验证实验。实验结果表明KSVD算法在恢复相似度和平均表示误差这两个指标上均优于MOD算法。
2)训练样本集及词典构建算法对超分辨率重建性能的影响分析。词典的构建需要样本集的训练,训练集一般分为两类：(1)自然图像训练集；(2)与待重建图像相关的训练集。将这两种训练集分别利用KSVD和MOD算法构建两类词典,并进行超分辨率重建。实验结果表明基于KSVD算法超分辨率重建的信噪比和相似度都高于MOD算法；训练集与待重建图像越相近,信噪比和相似度就越高。
3)改进的基于稀疏表示的彩色图像超分辨率重建方法。将低分辨率图像的RGB模式转换成YCbCr模式,利用KSVD算法构建Y、Cb、Cr三通道词典,分别对三个通道进行图像的超分辨率重建。实验结果表明与单独的Y分量重建以及R、G、B三通道重建方法相比较,本文算法重建的信噪比和相似度都有了提高。
4)基于几何局部自适应性锐化(GLAS)的图像后处理。针对重建后图像边缘模糊现象,采用GLAS算法进行图像后处理,根据图像的局部轮廓构建不同形状的核函数进行各向异性图像增强,实验取得较好效果。
The purpose of image super-resolution reconstruction is to reconstruct a high-resolution image or sequence from a single image or multiple low-resolution images which is based on signal processing techniques.lt can be classified into single image super-resolution reconstruction and multiple images super-resolution reconstruction. This thesis focus on single image super-resolution reconstruction algorithms.Sparse representation based single super-resolution reconstruction technique is one of the hot topics in the field of image processing.The key technologies include sparse matrix computing and dictionary construction as well as related post-processing techniques. Based on the analysis of dictionary construction algorithms'performance and the effect of the training sample sets on reconstruction quality,an improved color image super-resolution reconstruction method based on sparse representation is proposed,and a post-processing algorithm is used to enhance reconstructed images.The main work are as follows:
1) Performance verification of the dictionary construction algorithms.Two typical dictionary construction algorithms are implemented and the verification tests are conducted.The experimental results show that the KSVD algorithm outperforms MOD algorithm in respect of the relative number of correctly recovered atoms and the average representation error.
2) Influence analysis of training sample sets and dictionary construction algorithms on the performance of super-resolution reconstruction.The construction of dictionary needs training sample sets, the training sets generally include two categories:(1) natural images training set;(2) the training set related to the image which is to be reconstructed. Two types of dictionaries are constructed respectively from two training sets with KSVD and MOD algorithms, and super-resolution reconstruction tests are conducted based on the two trained dictionaries. The experiment results show that reconstructed images based on the dictionary trained by the KSVD algorithm are better than the one trained by the MOD algorithm in respect of the peak signal to noise ratio(PSNR) and structural similarity (SSIM),and the more similar training set to the image which is to be reconstructed, the higher PSNR and SSIM are.
3) Proposing an improved method of color image super-resolution reconstruction algorithm based on sparse representation.The image to be reconstructed is firstly converted the RGB mode to the YCbCr mode,then the Y, Cb and Cr channel dictionaries are trained with the KSVD algorithm,and finally super-resolution reconstruction are performed on the three channels. The experiment results show that, compared with the separate Y component of the reconstruction algorithm and the R, G and B channel reconstruction algorithm, the proposed algorithm has better performance on PSNR and SSIM.
4) Using a geometric locally adaptive sharpening (GLAS) based image post-processing algorithm to enhance the reconstructed image. For the reason that the reconstructed image edge is always blurred, a GLAS algorithm is used to enhance the image edges. The kernel functions are constructed according to the different shapes and sizes of the local structure of the image,and then are used to perform anisotropic filtering on the input image.The experimental results show that post-processing is necessary and can improve the reconstructed image quality numerically and visually.
1)词典构建算法性能验证。实现了两种典型的词典构建算法,并进行了性能验证实验。实验结果表明KSVD算法在恢复相似度和平均表示误差这两个指标上均优于MOD算法。
2)训练样本集及词典构建算法对超分辨率重建性能的影响分析。词典的构建需要样本集的训练,训练集一般分为两类：(1)自然图像训练集；(2)与待重建图像相关的训练集。将这两种训练集分别利用KSVD和MOD算法构建两类词典,并进行超分辨率重建。实验结果表明基于KSVD算法超分辨率重建的信噪比和相似度都高于MOD算法；训练集与待重建图像越相近,信噪比和相似度就越高。
3)改进的基于稀疏表示的彩色图像超分辨率重建方法。将低分辨率图像的RGB模式转换成YCbCr模式,利用KSVD算法构建Y、Cb、Cr三通道词典,分别对三个通道进行图像的超分辨率重建。实验结果表明与单独的Y分量重建以及R、G、B三通道重建方法相比较,本文算法重建的信噪比和相似度都有了提高。
4)基于几何局部自适应性锐化(GLAS)的图像后处理。针对重建后图像边缘模糊现象,采用GLAS算法进行图像后处理,根据图像的局部轮廓构建不同形状的核函数进行各向异性图像增强,实验取得较好效果。
The purpose of image super-resolution reconstruction is to reconstruct a high-resolution image or sequence from a single image or multiple low-resolution images which is based on signal processing techniques.lt can be classified into single image super-resolution reconstruction and multiple images super-resolution reconstruction. This thesis focus on single image super-resolution reconstruction algorithms.Sparse representation based single super-resolution reconstruction technique is one of the hot topics in the field of image processing.The key technologies include sparse matrix computing and dictionary construction as well as related post-processing techniques. Based on the analysis of dictionary construction algorithms'performance and the effect of the training sample sets on reconstruction quality,an improved color image super-resolution reconstruction method based on sparse representation is proposed,and a post-processing algorithm is used to enhance reconstructed images.The main work are as follows:
1) Performance verification of the dictionary construction algorithms.Two typical dictionary construction algorithms are implemented and the verification tests are conducted.The experimental results show that the KSVD algorithm outperforms MOD algorithm in respect of the relative number of correctly recovered atoms and the average representation error.
2) Influence analysis of training sample sets and dictionary construction algorithms on the performance of super-resolution reconstruction.The construction of dictionary needs training sample sets, the training sets generally include two categories:(1) natural images training set;(2) the training set related to the image which is to be reconstructed. Two types of dictionaries are constructed respectively from two training sets with KSVD and MOD algorithms, and super-resolution reconstruction tests are conducted based on the two trained dictionaries. The experiment results show that reconstructed images based on the dictionary trained by the KSVD algorithm are better than the one trained by the MOD algorithm in respect of the peak signal to noise ratio(PSNR) and structural similarity (SSIM),and the more similar training set to the image which is to be reconstructed, the higher PSNR and SSIM are.
3) Proposing an improved method of color image super-resolution reconstruction algorithm based on sparse representation.The image to be reconstructed is firstly converted the RGB mode to the YCbCr mode,then the Y, Cb and Cr channel dictionaries are trained with the KSVD algorithm,and finally super-resolution reconstruction are performed on the three channels. The experiment results show that, compared with the separate Y component of the reconstruction algorithm and the R, G and B channel reconstruction algorithm, the proposed algorithm has better performance on PSNR and SSIM.
4) Using a geometric locally adaptive sharpening (GLAS) based image post-processing algorithm to enhance the reconstructed image. For the reason that the reconstructed image edge is always blurred, a GLAS algorithm is used to enhance the image edges. The kernel functions are constructed according to the different shapes and sizes of the local structure of the image,and then are used to perform anisotropic filtering on the input image.The experimental results show that post-processing is necessary and can improve the reconstructed image quality numerically and visually.
引文
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[2]苏红旗,范郭亮.图像超分辨率重建技术综述.计算机技术与发展.2011,21(5)：124-127.
[3]陶洪久,饶俊飞,周祖德.单幅图的超分辨率重建方法.武汉理工大学学报(交通科学与工程版).2005,(4)：943-946.
[4]Tsai RY,Huang AK.Multiframe image restoration and registration. In Advances in Computer Vision and Image Proeessing.1984,5:317-339.
[5]Peleg S, Keren D, Schweitzer L. Improving image resolution using subpixel motion. Patter Recognition Letters.1987,5(3):223-226.
[6]Stark H, Oskoui P. High-resolution image recovery from image-plane arrays, using convex projections. Journal of the Optical Society of America.1989,6(11):1715-1726.
[7]Kere D, Peleg S. Image sequence enhancement using sub-pixel displacement.The IEEE Conference on Computer Vision and Pattern Recongnition,Michigan,1988:742-746.
[8]Schultz R, Stevenson R. Extraction of high-resolution frames from video sequences. IEEE Transactions on Image Processing.1996,5(6):996-1011.
[9]Elad M, Feuer A.Super-resolution reconstruction of an image.Proceedings of the 19th IEEE Conference, Israel,1996:391-394.
[10]Freeman W, Pasztor E C, Carmichael O T. Learning low-level vision. Internation Jou-rnal of Computer Vision.2000,40(1):25-47.
[11]Elad M,Feuer A.Restoration of a single super-resolution image from several blurred noisy and understand measured images.IEEE TransactionsImage Processing. 1997,6(12):1646-1658.
[12]Nguyen N, Milanfarp, Golub G.Efficient generalized cross-validation with applic-ation to parametric image restoration and resolution enhancement.IEEE Transactions on Image Processing.2001,10(9):1299-1308.
[13]Lee E, Kang M G. Regularized adaptived high-resolution image reconstruction considering inaccurate subpixel registration.IEEE Transaction on Image Processing. 2003,12(7):826-837.
[14]Donoho D. L, Elad M, Temlyakov. Stable recovery of sparse overcomplete represent-ations in the presence of noise.IEEE Transaction on Information Theory.2006, 52(1):6-18.
[15]Kang M,Chaudhuri S.Super-resolution image reconstruction. IEEE Signal Proce-ssing Magazine.2003,20 (3):19-20.
[16]Park S C,Park M K, Kang M G.Super-resolution image reconstruction:a technical overview. IEEE Signal Processing Magine.2006,20(3):21-36.
[17]Farsiu S, Robinson D, Elad M et al. Advances and challenges in super-resolution. International Journal of Imaging Systems and Technology.2004,14(2):47-57.
[18]Freeman W T,Jones T R, Pasztor E C. Example based superresolution. IEEE Computer Graphics and Application.2002,22 (2):56-65.
[19]Chang H, Yeung D, Xiong Y. Super-resolution through neighbor embedding. Proceed-ing of IEEE Conference CVPR, Washington,2004:275-282.
[20]Ni K, Kumar S, Vasconcelos N et al. Single image super-resolution based on support vector regression. Proceedings of the IEEE Internaional Conference on Acoustics, Speech and Single Processing, France,2006:601-604.
[2l]Hiroyuki Takeda,Peyman Milanfar,Matan Protter. Super-resolution without expli-cit subpixel motion estimation. IEEE Transactions on Image Processing.2009,18(9): 1958-1975.
[22]Yang J C,Wright J.Huang T et al.Image super-resolution via sparse representa-tion. IEEE Transactions on Image Processing.2010,19(11):2861-2873.
[23]Donoho D. L, Elad M. Optimally sparse representation in general dictionaries via minimization. Proceeding of the National Academy of Science.2003,100(5):2179-2202.
[24]Ophir B.Lustig M,Elad M. Multi-scale dictionary learning using wavelets. IEEE Selected Topics in Signal Processing.2011,5 (5):1014-1024.
[25]Ram I, Elad M, Cohen I. Generalized tree-based wavelet transform. IEEE Transacions on Signal Processing.2009,59(9):1199-4209.
[26]Donoho D. L, Elad M. On the stabi lity of the basis pursuit in the presence of noise. EURASIP Signal Processing Journal.2006,86(3):511-532.
[27]Protter M, Elad M. Image sequence denoising via sparse and redundant representa-tions. IEEE Transactions on Image Processing.2009,18(1):27-36.
[28]Protter M,Elad M, Takeda H et al.Generalizing the non-local means to super resolu-tion reconstruction. IEEE Transactions Image Processing.2009,18(1):36-51.
[29]Yang J, Yu K, Huang T. S. Efficient highly overeomplete sparse coding using mixture model.11th European Conference on Computer Vision, Greece,2010:1-15.
[30]Chen S, Donoho D I., Sauners M. Atomic decomposition by basis pursuit. SIMA REVIFW. 2001,13(1):129-159.
[31]H. Chang, D. Y. Yeung, and Y. Xiong. Super-resulution through neighbour embedding. IEEE Comuter Society Conference on Computer Vision and Pattern Recognition, 2004,1:275-282.
[32]Mairal J, Elad M, Sapiro G. Sparse Representation for Color Image Restoration. IEEE Transactions on Image Processing,2008,17 (1):53-69.
[33]Wang J. Zhu S. Gong Y. Resolution enhancement based on learning the sparse association of image patches. Pattern Recognition Letters,2010,31(1):1-10.
[34]付怀正.基于稀疏表示的彩色图像超分辨率重建算法研究：(硕士学位论文).汕头：汕头大学,2010.
[35]基于联合稀疏近似的彩色图像超分辨率重建.光电子.激光,2011,22(8)：1241-1245.
[36]工建英,尹忠科,张春梅.信号与图像的系数分解及初步应用.成都：西南交通大学出版社,2006.
[37]Bruno,OLshausen B A,Field D J.Emergence of simple-cell receptive rield proper-ties by Learning a sparse code for natural images. Nature.1996,381(13):607-609.
[38]蔡泽民,赖剑煌.一种基于超完备字典学习的图像去噪方法.电子学报.2009,37(2)：347-350.
[39]张春梅,尹忠科,肖明霞.基于冗余字典的信号超完备表示与稀疏分解.科学通报.2006,51(6)：628-633.
[40]Onur G, Guleryuz. On missing data prediction using sparse signal models:a compare-sion of atomic decompositions with iterated denoising.SPIE Conference, Sandiego, 2005:1-12.
[41]黄婧,李金宗.基于全局运动模型配准的图像超分辨重建.中国图像图形学报.2007,12(8)：1354-1358.
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