光滑l_p范数压缩感知图像重构优化算法
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摘要
针对已有压缩感知重构算法重构精度不高、消耗时间长的问题,在研究lp范数和光滑l0范数压缩感知重构算法的基础上提出改进算法。通过极大熵函数构造一种光滑函数来逼近最小lp范数,对解序列进行离散化来近似最小lp范数的最优解,结合图像分块压缩感知技术(BCS),在MATLAB中对测试图像进行仿真实验。结果表明,与传统的BOMP(Block Orthogonal Matching Pursuit)算法和IRLS(Iteratively Reweighted Least Squares)算法相比,改进后的算法不仅提高了重构精度,而且大大降低运行时间。
Aiming at the problem of low precision and long time consuming of the existing compressed sensing reconstruction algorithms, an improved algorithm is proposed based on the research of lpnorm and smooth l0 norm reconstruction algorithm. A smooth function is constructed with a maximum entropy function to approximate the minimum lp norm, then the solution sequence is discretized to approximate the optimal solution of the minimum lpnorm. Combined with image block compressed sensing technology. The test images are simulated in MATLAB. The results show that the proposed algorithm not only improves the reconstruction accuracy, but also greatly reduces the running time, compared to the traditional block orthogonal matching pursuit algorithm and the Iteratively Reweighted Least Squares(IRLS)algorithm.
Aiming at the problem of low precision and long time consuming of the existing compressed sensing reconstruction algorithms, an improved algorithm is proposed based on the research of lpnorm and smooth l0 norm reconstruction algorithm. A smooth function is constructed with a maximum entropy function to approximate the minimum lp norm, then the solution sequence is discretized to approximate the optimal solution of the minimum lpnorm. Combined with image block compressed sensing technology. The test images are simulated in MATLAB. The results show that the proposed algorithm not only improves the reconstruction accuracy, but also greatly reduces the running time, compared to the traditional block orthogonal matching pursuit algorithm and the Iteratively Reweighted Least Squares(IRLS)algorithm.
引文
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[12]森干.基于稀疏压缩感知的医学图像重构算法的研究[J].科技通报,2015(5):53-57.
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[14]赵瑞珍,林婉娟,李浩,等.基于光滑l0范数和修正牛顿法的压缩感知重建算法[J].计算机辅助设计与图形学学报,2012,24(4):478-484.
[15]蒋沅,苗生伟,罗华柱,等. lp范数压缩感知图像重建优化算法[J].中国图象图形学报,2017,22(4):435-442.
[16] Mohimani H,Zadeh M,Jutten C.A fast approach for overcomplete sparse decomposition based on smoothed l0norm[J].IEEE Transactions on Signal Processing,2014,40(10):564-568.
[17]颜世建.求解极大极小问题的调节熵函数法的收敛性[J].南京师大学报(自然科学版),2003,26(2):15-19.
[18]杨鹰,孔玲君.基于光滑l0范数压缩感知的多光谱图像去马赛克算法[J].光电子·激光,2017,28(6):674-679.
[2] Tsaig Y,Donoho D L.Extensions of compressed sensing[J].Signal Processing,2005,86(3):549-571.
[3] Dai Wei,Milenkovic O.Subspace pursuit for compressive sensing signal reconstruction[J].IEEE Transactions on Information Theory,2009,55(5):2230-2249.
[4]沈燕飞,李锦涛,朱珍民,等.基于非局部相似模型的压缩感知图像恢复算法[J].自动化学报,2015(2):261-272.
[5]祝文娟,严涛.基于熵函数的梯度型算法求解绝对值方[J].合肥师范学院学报,2016,34(3):1-4.
[6]刘效勇,曹益平,卢佩.基于压缩感知的光学图像加密技术研究[J].光学学报,2014(3):91-99.
[7]汪浩然,夏克文,牛文佳.分段正交匹配追踪(StOMP)算法改进研究[J].计算机工程与用,2017,53(16):55-61.
[8]李珅,马彩文,李艳,等.压缩感知重构算法综述[J].红外与激光工程,2013,42(S1):225-232.
[9]程德强,高凌志,陈亮亮,等.自适应多尺度分块压缩感知算法[J].中国图象图形学报,2017,22(9):1175-1182.
[10]李新颖,彭静,刘玉红,等.基于压缩感知的图像重构算法研究[J].自动化与仪器表,2015(7):152-154.
[11]杜佳兵,唐刚,王华庆.基于信号空间压缩感知算法的机械故障诊断[J].北京化工大学学报(自然科学版),2017,44(5):85-89.
[12]森干.基于稀疏压缩感知的医学图像重构算法的研究[J].科技通报,2015(5):53-57.
[13] Chartrand R,Yin W.Iteratively reweighted algorithms for compressive sensing[C]//IEEE International Conference on Acoustics,Speech and Signal Processing,2008:1089-1097.
[14]赵瑞珍,林婉娟,李浩,等.基于光滑l0范数和修正牛顿法的压缩感知重建算法[J].计算机辅助设计与图形学学报,2012,24(4):478-484.
[15]蒋沅,苗生伟,罗华柱,等. lp范数压缩感知图像重建优化算法[J].中国图象图形学报,2017,22(4):435-442.
[16] Mohimani H,Zadeh M,Jutten C.A fast approach for overcomplete sparse decomposition based on smoothed l0norm[J].IEEE Transactions on Signal Processing,2014,40(10):564-568.
[17]颜世建.求解极大极小问题的调节熵函数法的收敛性[J].南京师大学报(自然科学版),2003,26(2):15-19.
[18]杨鹰,孔玲君.基于光滑l0范数压缩感知的多光谱图像去马赛克算法[J].光电子·激光,2017,28(6):674-679.