空间变化模糊的图像复原算法
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摘要
传统的空间不变的模糊图像复原算法无法对空间变化图像取得良好的复原效果,空间变化的图像复原算法能够较好地复原图像,增强复原图像的可读性。新算法使用奇异值分解法将模糊核分解为基滤波器和系数滤波器的线性组合,提出一种总变分和小波框架双正则化模型。并使用ADMM算法将原问题分解为易于求解的子问题进行独立求解,使得算法能快速迭代收敛,在迭代过程中完成图像的复原与优化。实验结果表明:对于空间变化的模糊图像,提出的新算法能够较好地去模糊,取得较高的峰值信噪比和结构相似度,在主观评价上也具有良好的视觉效果。
When the traditional spatial invariant restoration algorithm cannot handle well the images blurred in space-variant way, the space-variant algorithm can restore the blurred images better and enhance readability of restored images. In this paper, singular value decomposition is used to decompose PSF into linear combination of base filter and coefficient filter, and a new regularization model combining total variation and wavelet frame is proposed. The ADMM algorithm is used to converts the complex optimization problem to several sub problems, which makes the algorithm can converge fast. The image restoration and optimization are completed in the iterative process. The experimental results show that the proposed algorithm improves PSNR and SSIM. It has the better image restoration quality in visual effect.
When the traditional spatial invariant restoration algorithm cannot handle well the images blurred in space-variant way, the space-variant algorithm can restore the blurred images better and enhance readability of restored images. In this paper, singular value decomposition is used to decompose PSF into linear combination of base filter and coefficient filter, and a new regularization model combining total variation and wavelet frame is proposed. The ADMM algorithm is used to converts the complex optimization problem to several sub problems, which makes the algorithm can converge fast. The image restoration and optimization are completed in the iterative process. The experimental results show that the proposed algorithm improves PSNR and SSIM. It has the better image restoration quality in visual effect.
引文
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[17] 易丽娅,鲁晓磊,王进军,等.图像复原的Bregman迭代双正则化方法[J].中国图象图形学报,2011,16(3):350-356.
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[2] TRUSSELL H, HUNT B. Image restoration of space variant blurs by sectioned methods[C]//Acoustics, Speech, and Signal Processing. New York: IEEE,1978:196-198.
[3] TEZAUR R, KAMATA T, LI H, et al. A system for estimating optics blur PSFs from test chart images[C]//SPIE/IS &T Electronic Imaging. San Francisco:International Society for Optics and Photonics,2015:458-463.
[4] HIRSCH M, SRA S, SCH?LKOPF B, et al. Efficient filter flow for space-variant multiframe blind deconvolution[C]//Computer Vision and Pattern Recognition (CVPR). New York: IEEE,2010:607-614.
[5] POPKIN T, CAVALLARO A, HANDS D. Accurate and efficient method for smoothly space-variant gaussian blurring[J].IEEE transactions on image processing,2010,19(5):1362-1370.
[6] MIRAUT D, PORTILLA J. Efficient shift-variant image restoration using deformable filtering (Part I)[J].EURASIP journal on advances in signal processing,2012(1):100.
[7] SROUBEK F, KAMENICKY J, LU Y M. Decomposition of space-variant blur in image deconvolution[J].IEEE signal processing letters,2016,23(3):346-350.
[8] 金燕,王卫静.基于稀疏优化字典的图像去噪算法[J].浙江工业大学学报,2017,45(3):320-324.
[9] 徐志江,安晟,卢为党.基于稀疏表达和暗通道的图像去雾霾算法[J].浙江工业大学学报,2017,45(3):315-319.
[10] MALGOUYRES F. A framework for image deblurring using wavelet packet bases[J].Applied and computational harmonic analysis,2002,12(3):309-331.
[11] CHAN R H, CHAN T F, SHEN L, et al. Wavelet algorithms for high-resolution image reconstruction[J].SIAM journal on scientific computing,2003,24(4):1408-1432.
[12] 彭宏,韩露莎,王辉,等.基于小波变换与多帧平均法融合的背景提取[J].浙江工业大学学报,2013,41(2):228-231.
[13] CHAN R H, CHAN T F, SHEN L, et al. Wavelet deblurring algorithms for spatially varying blur from high-resolution image reconstruction[J].Linear algebra and its applications,2003,366:139-155.
[14] BIOUCAS-DIAS J M, FIGUEIREDO M A T. An iterative algorithm for linear inverse problems with compound regularizers[C]//15th IEEE International Conference on Image Processing. New York: IEEE,2008:685-688.
[15] MA S, YIN W, ZHANG Y, et al. An efficient algorithm for compressed MR imaging using total variation and wavelets[C]//Computer Vision and Pattern Recognition. New York: IEEE,2008:1-8.
[16] PERONA P. Deformable kernels for early vision[J].IEEE transactions on pattern analysis and machine intelligence,1995,17(5):488-499.
[17] 易丽娅,鲁晓磊,王进军,等.图像复原的Bregman迭代双正则化方法[J].中国图象图形学报,2011,16(3):350-356.
[18] WANG Y, YANG J, YIN W, et al. A new alternating minimization algorithm for total variation image reconstruction[J].SIAM journal on imaging sciences,2008,1(3):248-272.