基于方向自适应观测与AMP的小波域图像压缩感知
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摘要
为了解决现有的基于近似消息传递(AMP)的图像压缩感知(CS)算法通常需要构建大尺寸观测矩阵的问题,研究了基于方向自适应观测与AMP的图像小波域压缩感知方案。针对传统变换域图像压缩感知方案采用的逐列观测、逐列重构方式的缺点,设计了一种基于图像空间相关性的方向自适应小波域压缩观测方法。进而,结合局部自适应维纳滤波,设计了一种基于AMP的小波系数子带压缩感知重构算法,能够在稀疏度未知的情况下以子带为单位实现图像小波系数的重建。仿真实验结果表明,与现有的图像小波域压缩感知方案相比,本文方案的重建图像质量较高;与现有的直接对整幅图像进行观测与重构的AMP方案相比,本文方案能够有效降低图像重建算法的运行时间。
Existing image compressed sensing(CS) algorithms based on approximate message passing(AMP) usually measure the image as a whole. Very large measurement matrix would be stored and transmitted. To solve this problem, this paper studies the image compressed sensing algorithm in wavelet domain based on direction-adaptive measurement and AMP. When the coefficient matrix is measured column by column, dependencies among columns are ignored. Here, a direction-adaptive measurement method in wavelet domain is designed, based on the dependencies among both columns and rows. Further, a new AMP algorithm is proposed to reconstruct wavelet coefficient subbands based on local adaptive Wiener filtering. It does not need the sparsity as a priori. Simulation results show that the proposed new scheme can achieve higher image reconstruction quality compared to existing CS schemes in wavelet domain and spends shorter running time compared to existing AMP schemes which measure and reconstruct the image as a whole.
Existing image compressed sensing(CS) algorithms based on approximate message passing(AMP) usually measure the image as a whole. Very large measurement matrix would be stored and transmitted. To solve this problem, this paper studies the image compressed sensing algorithm in wavelet domain based on direction-adaptive measurement and AMP. When the coefficient matrix is measured column by column, dependencies among columns are ignored. Here, a direction-adaptive measurement method in wavelet domain is designed, based on the dependencies among both columns and rows. Further, a new AMP algorithm is proposed to reconstruct wavelet coefficient subbands based on local adaptive Wiener filtering. It does not need the sparsity as a priori. Simulation results show that the proposed new scheme can achieve higher image reconstruction quality compared to existing CS schemes in wavelet domain and spends shorter running time compared to existing AMP schemes which measure and reconstruct the image as a whole.
引文
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[2]Donoho D.Compressed sensing[J].IEEE Transactions on Information Theory,2006,52(4):1289-1306
[3]Donoho D,Maleki A,Montanari A.Message passing algorithms for compressed sensing[J].Proceedings of the National Academy of Sciences of the United States of America,2009,106(45):18914-18919
[4]Bayati M,Montanari A.The dynamics of message passing on dense graphs,with applications to compressed sensing[J].IEEE Transactions on Information Theory,2011,57(2):764-785
[5]Donoho D,Maleki A,Montanari A.Message passing algorithms for compressed sensing I:motivation and construction[C].In:Proceedings of the IEEE Information Theory Workshop,Cairo,Egypt,2010.1-5
[6]Donoho D,Maleki A,Montanari A.Message passing algorithms for compressed sensing II:analysis and validation[C].In:Proceedings of the IEEE Information Theory Workshop,Cairo,Egypt,2010.6-10
[7]Schniter P.Turbo reconstruction of structured sparse signals[C].In:Proceedings of the 44th Annual Conference on Information Science and Systems,Princeton,USA,2010.1-6
[8]Som S,Schniter P.Compressive imaging using approximate message passing and a Markov-tree prior[J].IEEETransactions on Signal Processing,2012,60(7):3439-3448
[9]Tan J,Ma Y,Baron D.Compressive imaging via approximate message passing with image denoising[J].IEEETransactions on Signal Processing,2015,63(8):2085-2092
[10]Metzle C,Maleki A,Baraniuk R.From denoising to compressed sensing[J].IEEE Transactions on Information Theory,2016,62(9):5117-5144
[11]司菁菁,程银波.基于近似消息传递与卡通纹理模型的图像重构[J].系统工程与电子技术,2017,39(6):119-123
[12]程银波,司菁菁.基于近似消息传递的小波域图像压缩感知[J].燕山大学学报,2017,41(6):516-520,527
[13]岑翼刚,陈晓方,岑丽辉,等.基于单层小波变换的压缩感知图像处理[J].通信学报,2010,31(8A):52-55
[14]吴巧玲,倪林,何德龙.基于非下采样contourlet变换的压缩感知图像重建[J].中国科技大学学报,2012,42(2):87-91
[15]Do T,Gan L,Nguyen N,et al.Sparsity adaptive matching pursuit algorithm for practical compressed sensing[C].In:Proceedings of the 42nd Asilomar Conference on Signals,Systems and Computers.Pacific Grove,USA,2008.581-587