级联模型展开与残差学习的压缩感知重构
|
摘要
基于传统优化模型展开的深度网络由于集成了深度学习与传统优化方法的优点,具有良好的可解释性,在当前图像处理与计算机视觉领域得到广泛关注.提出了一种级联模型展开与残差学习的图像压缩感知重构深度网络框架,以实现重构图像质量的进一步改善.第一级的基于模型展开的深度网络根据输入的压缩测量值得到初始的重构图像,第二级的深度残差网络对初始重构图像进行去噪处理,最终得到高质量的重构结果.该两级级联网络的训练分别独立完成,训练过程简单易实现,将ADMM-Net与Res Net级联实现对磁共振图像重构,将ISTA-Net+与Res Net级联实现对自然图像重构.大量实验结果比较验证了所提出方法的有效性.
Deep networks based on unfolding conventional optimization model have been paid widely attention in many fields including image processing,computer vision and so on,because they not only combine the advantages of current deep leaning and conventional optimization-based approach,but also character well interpretability. A novel deep network architecture for compressive sensing image reconstruction is proposed by cascading model unfolding and residual learning,which aims to further improving the reconstructed image quality. The first stage of deep network is designed based on model unfolding to transform the compressed measurements of input into the initial reconstruction,and the second stage is a deep residual network to remove the noise in the initial reconstruction,consequently producing higher quality of reconstruction image. The training of the two-stage network is completed independently,which is simple and easy to conduct. Specifically,stacking the ADMM-Net and Res Net to reconstruct magnetic resonance imaging,and stacking the ISTA-Net+ and Res Net to reconstruct natural images. Extensive experimental results comparison demonstrates the effectiveness of the proposed method.
Deep networks based on unfolding conventional optimization model have been paid widely attention in many fields including image processing,computer vision and so on,because they not only combine the advantages of current deep leaning and conventional optimization-based approach,but also character well interpretability. A novel deep network architecture for compressive sensing image reconstruction is proposed by cascading model unfolding and residual learning,which aims to further improving the reconstructed image quality. The first stage of deep network is designed based on model unfolding to transform the compressed measurements of input into the initial reconstruction,and the second stage is a deep residual network to remove the noise in the initial reconstruction,consequently producing higher quality of reconstruction image. The training of the two-stage network is completed independently,which is simple and easy to conduct. Specifically,stacking the ADMM-Net and Res Net to reconstruct magnetic resonance imaging,and stacking the ISTA-Net+ and Res Net to reconstruct natural images. Extensive experimental results comparison demonstrates the effectiveness of the proposed method.
引文
[1]BARANIUK R G.Compressive sensing[Lecture Notes][J].IEEE Signal Processing Magazine,2007,24(4):118-121.
[2]焦李成,杨淑媛,刘芳.压缩感知回顾与展望[J].电子学报,2011,39(7):1651-1662.
[3]H Junzhou,C Chen,A Leon.Fast multi-contrast MRIreconstruction[J].Magnetic Resonance Imaging,2014,32(10):1344-1352.
[4]ZHAO B,HALDAR J P,CHRISTODOULOU A G,et al.Image reconstruction from highly undersampled(k,t)-space data with joint partial separability and sparsity constraints[J].IEEE Transactions on Medical Imaging,2012,31(9):1809-1820.
[5]MUN S,FOWLER J E.Block compressed sensing of images using directional transforms[C]//IEEE.IEEEInternational Conference on Image Processing.Snowbird:IEEE,2010:532-547.
[6]KIM Y,NADAR M S,BILGIN A.Compressed sensing using a Gaussian scale mixtures model in wavelet domain[C]//IEEE.IEEE International Conference on Image Processing.Hong Kong:IEEE,2010:3365-3368.
[7]LUSTIG M,DONOHO D,PAULY J M.Sparse MRI:The application of compressed sensing for rapid MRimaging.[J].Magnetic Resonance in Medicine,2007,58(6):1173-1182.
[8]ZHANG J,ZHAO D,ZHAO C,et al.Image compressive sensing recovery via collaborative sparsity[J].IEEEJournal on Emerging&Selected Topics in Circuits&Systems,2012,2(3):380-391.
[9]DONG W,SHI G,LI X,et al.Compressive sensing via non-local low-rank regularization[J].IEEE Transactions on Im-age Processing,2014,23(8):3618-3632.
[10]李佳,高志荣,熊承义,等.加权结构组稀疏表示的图像压缩感知重构[J].通信学报,2017,38(2):196-202.
[11]MOUSAVI A,PATEL A B,BARANIUK R G.A deep learning approach to structured signal recovery[C]//IEEE.IEEE Communication,Control,and Computing.Monticello:IEEE,2016:1336-1343.
[12]ILIADIS M,SPINOULAS L,KATSAGGELOS A K.Deep fully-connected networks for video compressive sensing[J].Digital Signal Processing,2018,72(1):9-18.
[13]KULKARNI K,LONIT S,TURAGA P et al.Recon Net:Non-Iterative Reconstruction of Images from Compressively Sensed Random Measurements[C]//IEEE.IEEE Conference on Computer Vision and Pattern Recognition.Las Vegas:IEEE,2016:449-458.
[14]HERSHEY J R,ROUX J L,WENINGER F.Deep unfolding:Model-based Inspiration of novel deep architectures[J].Computer Science,2014,2014arXiv1409.2574H.
[15]BORGERDING M,SCHNITER P.Onsager-corrected deep learning for sparse linear inverse problems[C]//IEEE.IEEE global conference on signal and information processing.Washington:IEEE 2016:227-231.
[16]YANG,Yan.Deep admm-net for compressive sensing MRI[C]//IEEE.Advances in Neural Information Processing Systems.Barcelona:IEEE,2016,10-18.
[17]JIAN,Zhang.ISTA-Net:Interpretable optimizationinspired deep network for image compressive sensing[C]//IEEE.IEEE Conference on Computer Vision and Pattern Recognition.Salt Lake City:IEEE,2018:1828-1837.
[18]ROMBERG J.Imaging via compressive samplingIntroduction to compressive sampling and recovery via convex programming[J].IEEE Signal Processing Magazine,2008,25(2):14-20.
[19]MALLAT S G,ZHANG Z.Matching pursuits with timefrequency dictionaries[J].IEEE Trans on Signal Processing,1993,41(12):3397-3415.
[20]TRIOO J,GILBERT A C.Signal recovery from random measurements via orthogonal matching pursuit[J].IEEETransactions on Information Theory,2007,53(12):4655-4666.
[21]杨真真,杨震,孙林慧.信号压缩重构的正交匹配追踪类算法综述[J].信号处理,2013,29(4):486-496.
[22]张宗念,李金徽,黄仁泰.迭代硬阈值压缩感知重构算法---IIHT[J].计算机应用,2011,31(8):2123-2125.
[23]熊承义,龚忠毅,高志荣,张梦杰.压缩感知图像的块子带自适应稀疏表示规则化重构[J].中南民族大学学报(自然科学版),2018,37(4):115-119.
[24]熊承义,陈仕长,高志荣,李世宇,金鑫,李治邦.基于自适应低秩去噪的近似消息传递压缩感知恢复[J].中南民族大学学报(自然科学版)2019,38(1):112-118.
[25]BOYD S,PARIKH N,CHU E,et al.Distributed optimization and statistical learning via the alternating direction method of multipliers[J].Foundations&Trends in Machine Learning,2011,3(1):1-122.
[26]HE K,ZHANG X,REN S,et al.Deep residual learning for image recognition[C]//IEEE.IEEEConference on Computer Vision and Pattern Recognition.Las Vegas:IEEE,2016:770-778.
[27]ZHANG K,CHEN Y,CHEN Y,et al.Beyond a gaussian denoiser:Residual learning of deep CNN for image denoising[J].IEEE Transactions on Image Procession,2017,26(7):3142-3155.
[28]LI C.An efficient algorithm for total variation regularization with applications to the single pixel camera and compressive Sensing[D].Houston:Rice University,2009.
[29]METZLER C A,MALEKI A,BARANIUK R G.From denoising to compressed sensing[J].IEEE Transactions on Information Theory,2016,62(9):5117-5144.
[30]CHEN C,TRAMEL E W,FOWLER J E.Compressedsensing recovery of images and video using multihypothesis predictions[C]//IEEE.IEEE Signals,Systems and Computers.Pacific Grove:IEEE,2012:1193-1198.
[2]焦李成,杨淑媛,刘芳.压缩感知回顾与展望[J].电子学报,2011,39(7):1651-1662.
[3]H Junzhou,C Chen,A Leon.Fast multi-contrast MRIreconstruction[J].Magnetic Resonance Imaging,2014,32(10):1344-1352.
[4]ZHAO B,HALDAR J P,CHRISTODOULOU A G,et al.Image reconstruction from highly undersampled(k,t)-space data with joint partial separability and sparsity constraints[J].IEEE Transactions on Medical Imaging,2012,31(9):1809-1820.
[5]MUN S,FOWLER J E.Block compressed sensing of images using directional transforms[C]//IEEE.IEEEInternational Conference on Image Processing.Snowbird:IEEE,2010:532-547.
[6]KIM Y,NADAR M S,BILGIN A.Compressed sensing using a Gaussian scale mixtures model in wavelet domain[C]//IEEE.IEEE International Conference on Image Processing.Hong Kong:IEEE,2010:3365-3368.
[7]LUSTIG M,DONOHO D,PAULY J M.Sparse MRI:The application of compressed sensing for rapid MRimaging.[J].Magnetic Resonance in Medicine,2007,58(6):1173-1182.
[8]ZHANG J,ZHAO D,ZHAO C,et al.Image compressive sensing recovery via collaborative sparsity[J].IEEEJournal on Emerging&Selected Topics in Circuits&Systems,2012,2(3):380-391.
[9]DONG W,SHI G,LI X,et al.Compressive sensing via non-local low-rank regularization[J].IEEE Transactions on Im-age Processing,2014,23(8):3618-3632.
[10]李佳,高志荣,熊承义,等.加权结构组稀疏表示的图像压缩感知重构[J].通信学报,2017,38(2):196-202.
[11]MOUSAVI A,PATEL A B,BARANIUK R G.A deep learning approach to structured signal recovery[C]//IEEE.IEEE Communication,Control,and Computing.Monticello:IEEE,2016:1336-1343.
[12]ILIADIS M,SPINOULAS L,KATSAGGELOS A K.Deep fully-connected networks for video compressive sensing[J].Digital Signal Processing,2018,72(1):9-18.
[13]KULKARNI K,LONIT S,TURAGA P et al.Recon Net:Non-Iterative Reconstruction of Images from Compressively Sensed Random Measurements[C]//IEEE.IEEE Conference on Computer Vision and Pattern Recognition.Las Vegas:IEEE,2016:449-458.
[14]HERSHEY J R,ROUX J L,WENINGER F.Deep unfolding:Model-based Inspiration of novel deep architectures[J].Computer Science,2014,2014arXiv1409.2574H.
[15]BORGERDING M,SCHNITER P.Onsager-corrected deep learning for sparse linear inverse problems[C]//IEEE.IEEE global conference on signal and information processing.Washington:IEEE 2016:227-231.
[16]YANG,Yan.Deep admm-net for compressive sensing MRI[C]//IEEE.Advances in Neural Information Processing Systems.Barcelona:IEEE,2016,10-18.
[17]JIAN,Zhang.ISTA-Net:Interpretable optimizationinspired deep network for image compressive sensing[C]//IEEE.IEEE Conference on Computer Vision and Pattern Recognition.Salt Lake City:IEEE,2018:1828-1837.
[18]ROMBERG J.Imaging via compressive samplingIntroduction to compressive sampling and recovery via convex programming[J].IEEE Signal Processing Magazine,2008,25(2):14-20.
[19]MALLAT S G,ZHANG Z.Matching pursuits with timefrequency dictionaries[J].IEEE Trans on Signal Processing,1993,41(12):3397-3415.
[20]TRIOO J,GILBERT A C.Signal recovery from random measurements via orthogonal matching pursuit[J].IEEETransactions on Information Theory,2007,53(12):4655-4666.
[21]杨真真,杨震,孙林慧.信号压缩重构的正交匹配追踪类算法综述[J].信号处理,2013,29(4):486-496.
[22]张宗念,李金徽,黄仁泰.迭代硬阈值压缩感知重构算法---IIHT[J].计算机应用,2011,31(8):2123-2125.
[23]熊承义,龚忠毅,高志荣,张梦杰.压缩感知图像的块子带自适应稀疏表示规则化重构[J].中南民族大学学报(自然科学版),2018,37(4):115-119.
[24]熊承义,陈仕长,高志荣,李世宇,金鑫,李治邦.基于自适应低秩去噪的近似消息传递压缩感知恢复[J].中南民族大学学报(自然科学版)2019,38(1):112-118.
[25]BOYD S,PARIKH N,CHU E,et al.Distributed optimization and statistical learning via the alternating direction method of multipliers[J].Foundations&Trends in Machine Learning,2011,3(1):1-122.
[26]HE K,ZHANG X,REN S,et al.Deep residual learning for image recognition[C]//IEEE.IEEEConference on Computer Vision and Pattern Recognition.Las Vegas:IEEE,2016:770-778.
[27]ZHANG K,CHEN Y,CHEN Y,et al.Beyond a gaussian denoiser:Residual learning of deep CNN for image denoising[J].IEEE Transactions on Image Procession,2017,26(7):3142-3155.
[28]LI C.An efficient algorithm for total variation regularization with applications to the single pixel camera and compressive Sensing[D].Houston:Rice University,2009.
[29]METZLER C A,MALEKI A,BARANIUK R G.From denoising to compressed sensing[J].IEEE Transactions on Information Theory,2016,62(9):5117-5144.
[30]CHEN C,TRAMEL E W,FOWLER J E.Compressedsensing recovery of images and video using multihypothesis predictions[C]//IEEE.IEEE Signals,Systems and Computers.Pacific Grove:IEEE,2012:1193-1198.