Fractional Total Variation Algorithm Based on Improved Non-local Means

doi:10.19678/j.issn.1000-3428.0049463

Abstract

Abstract:

The traditional total variation algorithm is mostly affected by the staircase effect in the variation process,so it causes texture loss and over-smoothing in the reconstructed image.Therefore,a reconstruction algorithm based on improved non-local means is proposed.The image texture information is preserved by introducing a fractional step model,and the Lagrangian gradient operator is updated by the non-local means filtering method,thereby reducing the computational complexity.Experimental results show that compared with the traditional TVAL3 algorithm,this algorithm can effectively reduce the running time and has better reconstruction performance.

Key words: compressive sensing, fractional differential, total variation, non-local means, staircase effect

摘要：

传统全变分算法在变分过程中多数会受到阶梯效应的影响，导致重构图像出现纹理缺失和过平滑。为此，提出一种基于改进非局部均值的重构算法。通过引入分数阶梯度模型保留图像纹理信息，利用非局部均值滤波法更新拉格朗日梯度算子，从而降低计算复杂度。实验结果表明，与传统TVAL3算法相比，该算法能够有效减少运行时间，具有较好的重构性能。

关键词: 压缩感知, 分数阶微分, 全变分, 非局部均值, 阶梯效应

CLC Number:

TP391

FENG Chenbo,QIN Yali,CHEN Hui,CHANG Liping,XUE Linlin. Fractional Total Variation Algorithm Based on Improved Non-local Means[J]. Computer Engineering, 2019, 45(4): 241-247.

封晨波,覃亚丽,陈辉,常丽萍,薛林林. 基于改进非局部均值的分数阶全变分算法[J]. 计算机工程, 2019, 45(4): 241-247.

/ / Recommend / Download Citations

URL: http://www.ecice06.com/EN/10.19678/j.issn.1000-3428.0049463

http://www.ecice06.com/EN/Y2019/V45/I4/241

References

［1］DONOHO D L.Compressed sensing［J］.IEEE Transactions on Information Theory,2006,52(4):1289-1306.
［2］CANDS E J.Compressive sampling［EB/OL］.［2017-10-20］.http://statweb.stanford.edu/~candes/papers/Compressive Sampling.pdf.
［3］CANDES E J,WAKIN M B.An introduction to compressive sampling［J］.IEEE Signal Processing Magazine,2008,25(2):21-30.
［4］DONOHO D L,TSAIG Y.Fast solution of L1-norm minimization problems when the solution may be sparse［J］.IEEE Transactions on Information Theory,2008,54(11):4789-4812.
［5］DONOHO D L.For most large underdetermined systems of linear equations the minimal L1-norm Solution is also the sparsest solution［EB/OL］.［2017-10-20］.https://onlinelibrary.wiley.com/doi/abs/10.1002/cpa.20132.
［6］LI W,LIU F,JIAO L,et al.A group matching pursuit for image reconstruction［J］.Image Communication,2016,49(C):47-62.
［7］ZHANG L,ZHOU W.Spectral gradient projection method for solving nonlinear monotone equations［J］.Journal of Computational and Applied Mathematics,2017,196(2):478-484.
［8］RAUHUT H,SCHNEIDER R,STOJANAC .Low rank tensor recovery via iterative hard thresholding［J］.Linear Algebra and Its Applications,2017,523:220-262.
［9］SELESNICK I.Total variation denoising via the moreau envelope［J］.IEEE Signal Processing Letters,2017,24(2):216-220.
［10］LI C,YIN W,JIANG H,et al.An efficient augmented Lagrangian method with applications to total variation minimization［J］.Computational Optimization and Applications,2013,56(3):507-530.
［11］ZHANG J,LIU S,XIONG R,et al.Improved total variation based image compressive sensing recovery by nonlocal regularization［C］//Proceedings of IEEE International Symposium on Circuits and Systems.Washington D.C.,USA:IEEE Press,2013:2836-2839.
［12］陈建,苏凯雄,杨秀芝,等.基于变分模型的块压缩感知重构算法［J］.通信学报,2016,37(1):100-109.
［13］ZHANG X,BURGER M,BRESSON X,et al.Bregmanized nonlocal regularization for deconvolution and sparse reconstruction［J］.SIAM Journal on Imaging Sciences,2010,3(3):253-276.
［14］DONG W,YANG X,SHI G.Compressive sensing via reweighted TV and nonlocal sparsity regularisation［J］.Electronics Letters,2013,49(3):184-186.
［15］WARREN R E,OSHER S J.Hyperspectral unmixing by the alternating direction method of multipliers［J］.Inverse Problems and Imaging,2017,9(3):917-933.
［16］XU S,ZHOU Y,XIANG H,et al.Remote sensing image denoising using patch grouping-based nonlocal means algorithm［J］.IEEE Geoscience and Remote Sensing Letters,2017,14(12):2275-2279.
［17］李博,谢巍.基于自适应分数阶微积分的图像去噪与增强算法［J］.系统工程与电子技术,2016,38(1):185-192.
［18］ATANGANA A,BALEANU D.New fractional derivatives with nonlocal and non-singular kernel:theory and application to heat transfer model［EB/OL］.［2017-10-20］.https://arxiv.org/ftp/arxiv/papers/1602/1602.03408.pdf.
［19］TAN J,XIONG J.A harnack inequality for fractional laplace equations with lower order terms［J］.Discrete and Continuous Dynamical Systems,2011,31(3):975-983.
［20］RAFEIRO H,SAMKO S.Fractional integrals and derivatives:mapping properties［J］.Fractional Calculus and Applied Analysis,2016,19(3):580-607.
［21］MA L,MOISAN L,YU J,et al.A stable method solving the total variation dictionary model with L∞ constraints［J］.Inverse Problems and Imaging,2014,8(2):507-535.
［22］海涛,席志红.基于改进复扩散耦合非局部均值滤波器的图像放大［J］.系统工程与电子技术,2016,38(5):1182-1188.
［23］张娜,刘辉,尚振宏,等.改进权重函数的非局部均值图像去噪算法［J］.计算机工程,2016,42(12):254-261.
［24］XIAO Y,YANG J.A fast algorithm for total variation image reconstruction from random projections［J］.Inverse Problems and Imaging,2017,6(3):547-563.

[1]	PAN Jinfeng, YIN Liju, GAO Mingliang, ZOU Guofeng. Low-Rank and Sparse Decomposition of Compressive Sensing Observation Signals [J]. Computer Engineering, 2022, 48(8): 234-239.
[2]	HAN Mengyan, LI Liangrong, JIANG Kai. Retinex Low-Illumination Image Enhancement Algorithm Based on Light Image Estimation [J]. Computer Engineering, 2021, 47(10): 201-206.
[3]	YU Mali,ZHANG Hai. HDR Imaging Based on Low-rank Matrix Completion and Total Variation Constraint [J]. Computer Engineering, 2019, 45(4): 262-266,274.
[4]	WANG Nan,LI Zhi,CHENG Xinyu,CHEN Yi,LUO Hao. Video Dual Watermarking Algorithm Based on Mean Ratio and Compressive Sensing [J]. Computer Engineering, 2019, 45(3): 250-255,261.
[5]	ZHANG Wenkun,WANG Xiyuan,SONG Jiaqian. Edge Detection Algorithm Based on Fractional Differential Difference and Gaussian Curvature Filtering [J]. Computer Engineering, 2019, 45(2): 213-219.
[6]	XIA Senlin,SUN Huaijiang,CHEN Beijia. Application of Welsch M-estimation in Video Reconstruction and Background Subtraction [J]. Computer Engineering, 2019, 45(1): 270-277.
[7]	GAO Yuan,JIA Ziting,QIN Pinle,WANG Lifang. Medical Image Fusion Based on Compressive Sensing and Adaptive PCNN [J]. Computer Engineering, 2018, 44(9): 224-229.
[8]	LI Yulong,LIU Renren,ZHAO Jinfeng,ZANG Lang,CAO Bin. Data Collection Method in Clustering Sensing Network Based on Compressive Sensing [J]. Computer Engineering, 2018, 44(10): 129-135.
[9]	LONG Ken,YAN Bingbing,LIU Yuezhen,DU Fei. Pilot Contamination Mitigation Algorithm in Massive MIMO Based on Spatial-Temporal Domain Compression [J]. Computer Engineering, 2017, 43(7): 141-145.
[10]	LIU Yang. Forwarding-tree Construction and Link Scheduling Algorithm for Data Collection [J]. Computer Engineering, 2017, 43(10): 82-90.
[11]	GUO Beibei,YI Sanli,HE Jianfeng,MIAO Ying,SHAO Dangguo. Improved Non-local Means Filtering Algorithm [J]. Computer Engineering, 2016, 42(7): 227-231.
[12]	CHEN Kangrun,LIU Yang,ZHANG Wei. Research on Low-complexity PAPR Reduction Algorithm in Radar-communication Integrated System [J]. Computer Engineering, 2016, 42(6): 86-90.
[13]	WANG Zan,XU Xiaorong,YAO Yingbiao. Bayesian Compressive Sensing Wideband Spectrum Detection Based on Energy Efficiency [J]. Computer Engineering, 2016, 42(3): 125-129.
[14]	ZHUANG Yanbin,WANG Zunzhi,XIAO Xianjian,ZHANG Xuewu. Video Compressive Sensing Reconstruction Algorithm Based on 3D Tree Structure and Bayesian Model [J]. Computer Engineering, 2016, 42(2): 266-271.
[15]	ZHANG Na,LIU Hui,SHANG Zhenhong,ZOU Binyi. Non-local Means Image Denoising Algorithm of Improved Weighting Function [J]. Computer Engineering, 2016, 42(12): 254-261.

Please choose a citation manager

Content to export