基于Curvelet变换的压缩传感超分辨率重建
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摘要
为了在无训练集的情况下,改善单帧退化图像的分辨率,实现了一种基于Curvelet变换和快速迭代收缩阈值法(FIST)的压缩传感超分辨率重建算法(Curvelet-FIST)。算法首先对低分辨率图像建立伪星形采样的采样方式,利用压缩传感理论,在Curvelet变换域,通过快速迭代收缩阈值法由采样值恢复出高分辨率图像。仿真实验表明,此超分辨率重建算法比传统的插值算法以及基于Wavelet变换和FIST的压缩传感重建算法(Wavelet-FIST)有更高的峰值信噪比。
In order to improve the resolution of single-frame degraded images under the condition of no any training set,we implemented a compressed sensing super-resolution reconstruction algorithm,called Curvelet-FIST,which is based on Curvelet transform and fast iterative threshold-shrinkage( FIST) algorithm. First,the algorithm sets up a sampling mode of pseudo-star-shape sampling on low-resolution images.Then by making use of the theory of compressed sensing,and in Curvelet transform domain,it restores the high-resolution image from sampling values through FIST algorithm. Simulation experiment showed that this super-resolution reconstruction algorithm,compared with traditional interpolation algorithm and the compressed sensing reconstruction algorithm based on Wavelet transform and FIST( Wavelet-FIST),has higher peak signal-to-noise ratio( PSNR).
In order to improve the resolution of single-frame degraded images under the condition of no any training set,we implemented a compressed sensing super-resolution reconstruction algorithm,called Curvelet-FIST,which is based on Curvelet transform and fast iterative threshold-shrinkage( FIST) algorithm. First,the algorithm sets up a sampling mode of pseudo-star-shape sampling on low-resolution images.Then by making use of the theory of compressed sensing,and in Curvelet transform domain,it restores the high-resolution image from sampling values through FIST algorithm. Simulation experiment showed that this super-resolution reconstruction algorithm,compared with traditional interpolation algorithm and the compressed sensing reconstruction algorithm based on Wavelet transform and FIST( Wavelet-FIST),has higher peak signal-to-noise ratio( PSNR).
引文
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[19]张莎,田逢春,谭洪涛.基于下采样的快速块匹配搜索算法及降噪应用[J].计算机应用,2010,30(10):2819-2822.
[2]Tai Y W,Liu S,Brown M S,et al.Super resolution using edge prior and single image detail synthesis[C]//Proceedings of 2010 IEEE Conference on Computer Vision and Pattern Recognition(CVPR 2010),San Francisco,USA,2010:2400-2407.
[3]樊博,杨晓梅,胡学姝.基于压缩感知的超分辨率图像重建[J].计算机应用,2013,33(2):480-483.
[4]Sen P,Darabi S.Compressive image super-resolution[C]//Conference Record of the 43rd Asilomar Conference on Signals Systems and Computers,California,USA,2009:1235-1242.
[5]Sun Y,Gu G,Sui X,et al.Single image super-resolution using compressive sensing with a redundant dictionary[J].IEEE Photonics Journal,2015,7(2):1-11.
[6]Baraniuk R G.Compressive sensing[J].IEEE Signal Processing Magezine,2007,24(4):118-121.
[7]Beck A,Teboulle M.A fast iterative shrinkage-thresholding algorithm for linear inverse problems[J].Siam Journal on Imaging Sciences,2009,2(1):183-202.
[8]焦淑红,唐琳,齐欢,等.迭代收缩阈值雷达前视成像方法[J].航空学报,2014,35(12):3384-3391.
[9]Candes E J,Donoho D L.Curvelets-a surprisingly effective nonadaptive representation for objects with edges[C]//Curves and Surface Fitting,Saint-Malo,France,1999:105-120.
[10]文奴,杨世植,崔生成.基于Curvelet-Wavelet变换高分辨率遥感图像降噪[J].浙江大学学报:工学版,2015,49(1):79-86.
[11]叶慧,孔繁锵.基于Curvelet变换的图像压缩感知重构[J].计算机工程,2014,40(2):233-236.
[12]Wang S,Huang T Z,Liu J,et al.An alternating iterative algorithm for image deblurring and denoising problems[J].Communications in Nonlinear Science&Numerical Simulation,2014,19(3):617-626.
[13]Candes E J,Romberg J,Tao T.Robust uncertainty principles:exact signal reconstruction from highly incomplete frequency information[J].IEEE Transactions on Information Theory,2006,52(2):489-509.
[14]Donoho D L,Elad M,Temlyakov V N.Stable recovery of sparse overcomplete representations in the presence of noise[J].IEEE Transactions on Information Theory,2006,52(1):6-18.
[15]Candes E J,Demanet L,Donoho D,et al.Fast discrete curvelet transforms[J].Siam Journal on Multiscale Modeling&Simulation,2005,5(3):861-899.
[16]练秋生,王艳.基于双树小波通用隐马尔可夫树模型的图像压缩感知[J].电子与信息学报,2010,32(10):2301-2306.
[17]Zhang L.Video coding based on compressive sensing via Co Sa MP[J].Journal of Donghua University:english Edition,2014,31(5):727-730.
[18]Wan T,Canagarajah N,Achim A.Compressive image fusion[C]//Proceedings of 15th IEEE International Conference on Image Processing(ICIP 2008),San Diego,USA,2008:1308-1311.
[19]张莎,田逢春,谭洪涛.基于下采样的快速块匹配搜索算法及降噪应用[J].计算机应用,2010,30(10):2819-2822.