一种基于单像素相机的压缩感知图像重建优化算法
|
摘要
基于压缩感知图像重构和单像素相机成像的基本原理,对单像素成像系统中的图像重建算法进行了改进优化。基于最小范数类优化算法,结合凸优化算法和非凸优化算法各自的优点,设计了一种逼近L0范数的数学模型,从而实现了从凸优化向非凸优化算法的迭代逼近,即逼近光滑L0范数算法。该新型算法以更高的效率和更大的概率逼近原始信号全局最优且尽可能稀疏的解。相较于传统压缩感知图像重建的贪婪类算法和最小范数类算法,该算法使压缩感知重建图像的质量和单像素相机的成像效果均得到了有效提升,并通过实验仿真和实际场景的成像实验验证了该优化算法的可行性。
Based on the basic principles of single-pixel camera imaging and compressed sensing image reconstruction,the image reconstruction algorithm of single-pixel camera was optimized.Based on the optimization algorithm of minimum norm and by combining the advantages of convex optimization and non-convex optimization,a mathematical model approximating L0 norm was designed to realize the iterative approximation from convex optimization to non-convex optimization,and a new algorithm approximating the smooth L0 norm algorithm was proposed.The proposed algorithm approximates the global optimal solution as sparse as possible with higher efficiency and greater probability.Compared with the traditional greedy algorithm and minimum norm algorithm,the new algorithm improves the quality of reconstructed images and imaging effectively,and its feasibility was verified by simulations and actual single-pixel imaging experiments.
Based on the basic principles of single-pixel camera imaging and compressed sensing image reconstruction,the image reconstruction algorithm of single-pixel camera was optimized.Based on the optimization algorithm of minimum norm and by combining the advantages of convex optimization and non-convex optimization,a mathematical model approximating L0 norm was designed to realize the iterative approximation from convex optimization to non-convex optimization,and a new algorithm approximating the smooth L0 norm algorithm was proposed.The proposed algorithm approximates the global optimal solution as sparse as possible with higher efficiency and greater probability.Compared with the traditional greedy algorithm and minimum norm algorithm,the new algorithm improves the quality of reconstructed images and imaging effectively,and its feasibility was verified by simulations and actual single-pixel imaging experiments.
引文
[1] Donoho D L.Compressed sensing[J].IEEE Trans.on Information Theory,2006,52(4):1289-1306.
[2] Candes E.Compressive sampling[C]//Proc.of the Inter.Congress of Mathematicians,2006:1433-1452.
[3] Foucart S, Rauhut H, Benedetto J J.A Mathematical Introduction to Compressive Sensing in Applied and Numerical Harmonic Analysis[M].New York:Birkhauser/Springer,2013.
[4] Stahl H,Mietzner J,Fischer R F H.A sub-nyquist radar system based on optimized sensing matrices derived via sparse rulers[C]//2015 3rd Inter.Workshop on Compressed Sensing Theory and Its Applications to Radar,Sonar and Remote Sensing(CoSeRa),2015:36-40.
[5] Boche H,Calderbank R,Kutyniok G,et al.Compressed Sensing and Its Applications[M].New York:Springer International Publishing,2015.
[6] Duarte M F,Davenport M A,Takhar D,et al.Single-pixel imaging via compressive sampling[J].IEEE Signal Proc.Magazine,2008,25(2):83-91.
[7] Tropp J A, Gilbert A C.Signal recovery from random measurements via orthogonal matching pursuit[J].IEEE Trans.Inf.Theory,2007,53:4655-4666.
[8] Candes E,Tao T.Near optimal signal recovery from random projections:Universal encoding strategies[C]//IEEE Trans.Inform.Theory,2006,52(12):5406-5425.
[9] Baraniuk R G.Compressive sensing[J].IEEE Signal Proc.Magazine,2007,24(4):118-121.
[10] Chen S S, DonohoDL, SaundersMA. Atomic decomposition by basis pursuit[J].SIAM Rev.,2001,43:129-159.
[11] Tropp J A,Gilbert A C.Signal recovery from random measurements via orthogonal matching pursuit[J].IEEE Trans.on Information Theory,2007,53(12):4655-4666.
[12] Abdel-Sayed M M,Khattab A,Abu-Elyazeed M F.Adaptive reduced-set matching pursuit for compressed sensing recovery[C]//IEEE Inter.Conf.on Image Processing,2016.
[13] Blumensath T,Davies M E.Iterative thresholding for sparse approximations[J].J.of Fourier Analysis and Applications,2008,14(5/6):629-654.
[14] Wang Q,Li D.Intelligent nonconvex compressive sensing using prior information for image reconstruction by sparse representation[J].Neurocomputing,2017,224:71-81.
[15] Mallat S,著.杨力华,戴道清,黄文良,等译.信号处理的小波导引[M].第2版.北京:机械工业出版社,2002.Mallat S.Yang Lihua,Dai Daoqing,Huang Wenliang,et al.transl.Signal Processing for Small Waveguide Guidance[M].2nd Edi.Beijing:China Machine Press,2002.
[16] Jiao Licheng,Tan Shan.Development and prospect of image multiscale geometric analysis[J].Acta Sinica Electronica,2003,31(12A):1975-1981.
[17] Needell D,Vershynin R.Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit[J].IEEE J.Sel.Top.Signal Process,2010(4):310-316.
[18] Chartrand R,Yin W.Iteratively reweighted algorithms for compressive sensing[R].CAAM Technical Reports,2008.
[2] Candes E.Compressive sampling[C]//Proc.of the Inter.Congress of Mathematicians,2006:1433-1452.
[3] Foucart S, Rauhut H, Benedetto J J.A Mathematical Introduction to Compressive Sensing in Applied and Numerical Harmonic Analysis[M].New York:Birkhauser/Springer,2013.
[4] Stahl H,Mietzner J,Fischer R F H.A sub-nyquist radar system based on optimized sensing matrices derived via sparse rulers[C]//2015 3rd Inter.Workshop on Compressed Sensing Theory and Its Applications to Radar,Sonar and Remote Sensing(CoSeRa),2015:36-40.
[5] Boche H,Calderbank R,Kutyniok G,et al.Compressed Sensing and Its Applications[M].New York:Springer International Publishing,2015.
[6] Duarte M F,Davenport M A,Takhar D,et al.Single-pixel imaging via compressive sampling[J].IEEE Signal Proc.Magazine,2008,25(2):83-91.
[7] Tropp J A, Gilbert A C.Signal recovery from random measurements via orthogonal matching pursuit[J].IEEE Trans.Inf.Theory,2007,53:4655-4666.
[8] Candes E,Tao T.Near optimal signal recovery from random projections:Universal encoding strategies[C]//IEEE Trans.Inform.Theory,2006,52(12):5406-5425.
[9] Baraniuk R G.Compressive sensing[J].IEEE Signal Proc.Magazine,2007,24(4):118-121.
[10] Chen S S, DonohoDL, SaundersMA. Atomic decomposition by basis pursuit[J].SIAM Rev.,2001,43:129-159.
[11] Tropp J A,Gilbert A C.Signal recovery from random measurements via orthogonal matching pursuit[J].IEEE Trans.on Information Theory,2007,53(12):4655-4666.
[12] Abdel-Sayed M M,Khattab A,Abu-Elyazeed M F.Adaptive reduced-set matching pursuit for compressed sensing recovery[C]//IEEE Inter.Conf.on Image Processing,2016.
[13] Blumensath T,Davies M E.Iterative thresholding for sparse approximations[J].J.of Fourier Analysis and Applications,2008,14(5/6):629-654.
[14] Wang Q,Li D.Intelligent nonconvex compressive sensing using prior information for image reconstruction by sparse representation[J].Neurocomputing,2017,224:71-81.
[15] Mallat S,著.杨力华,戴道清,黄文良,等译.信号处理的小波导引[M].第2版.北京:机械工业出版社,2002.Mallat S.Yang Lihua,Dai Daoqing,Huang Wenliang,et al.transl.Signal Processing for Small Waveguide Guidance[M].2nd Edi.Beijing:China Machine Press,2002.
[16] Jiao Licheng,Tan Shan.Development and prospect of image multiscale geometric analysis[J].Acta Sinica Electronica,2003,31(12A):1975-1981.
[17] Needell D,Vershynin R.Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit[J].IEEE J.Sel.Top.Signal Process,2010(4):310-316.
[18] Chartrand R,Yin W.Iteratively reweighted algorithms for compressive sensing[R].CAAM Technical Reports,2008.