基于改进非局部均值的分数阶全变分算法
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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。
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.
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.
引文
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[2] CANDèS 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.