基于e~p的DTV图像去噪模型
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摘要
针对纹理图像的去噪问题,通过分析全变分(TV)去噪模型与方向全变分(DTV)去噪模型,提出了一种具有鲁棒性的基于e~p的DTV去噪模型。为了刻画图像中的不同结构特征,该模型中DTV正则项的指数p由图像的结构来确定在(0,2)中自适应地选取。由于该模型是含有可分性算子的非光滑优化问题,可用交替方向乘子法(ADMM)求解,并能保证算法的收敛性。数值实验结果表明:与其他经典模型相比,提出的模型取得了更高的峰值信噪比和结构相似度,在去除噪声的同时能有效保持图像的细节信息。
For the problem of texture image denoising,by analyzing the advantages and disadvantages of the total variation(TV) denoising model and the directional total variation(DTV) denoising model,we propose a robust denoising model based on e~p directional total variation. In the proposed model,in order to efficiently characterize the different structural features in the image,the exponential p in the edge adaptive directional total variation regularization term can be availably chosen in(0,2) based on the structure in the image.Since the proposed model is a non-smooth convex optimization with separable operator,it can be solved by using the alternating direction method of multipliers(ADMM). Then the convergence of the numerical method can be efficiently kept. Compared with other classic models,numerical implementations show that the proposed model can achieve higher peak signal-to-noise ratio and structural similarity,and can effectively retain image details while removing noise.
For the problem of texture image denoising,by analyzing the advantages and disadvantages of the total variation(TV) denoising model and the directional total variation(DTV) denoising model,we propose a robust denoising model based on e~p directional total variation. In the proposed model,in order to efficiently characterize the different structural features in the image,the exponential p in the edge adaptive directional total variation regularization term can be availably chosen in(0,2) based on the structure in the image.Since the proposed model is a non-smooth convex optimization with separable operator,it can be solved by using the alternating direction method of multipliers(ADMM). Then the convergence of the numerical method can be efficiently kept. Compared with other classic models,numerical implementations show that the proposed model can achieve higher peak signal-to-noise ratio and structural similarity,and can effectively retain image details while removing noise.
引文
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[2]RUDIN L,OSHER S,FATEMI E.Nonlinear total variation based noise removal algorithms[J].Physica D:Non-linear Phenomena,1992,60(1-4):259-268.
[3]HOREV I,NADLER B,ARIAS-CASTRO E,et al.Detection of long edges on a computational budget:A sublinear approach[J].SIAM Journal on Imaging Science,2015,8(1):458-483.
[4]HU Y,ONGIE G,RAMANI S,et al.Generalized higher degree total variation(HDTV)regularization[J].IEEE Transactions on Image Processing,2014,23(6):2423-2435.
[5]BREDIES K,KUNISCH K,POCK T.Total generalized variation[J].SIAM Journal on Imaging Science,2012,3(3):492-526.
[6]COLL B,DURAN J,SBERT C.Half-linear regularization for nonconvex image restoration models[J].Inverse Problem and Imaging,2015,9(2):337-370.
[7]BAYRAM I,KAMASAK M.Directional total variation[J].IEEE Signal Processing Letters,2012,19(12):781-784.
[8]ZHANG H,WANG Y Q.Edge adaptive directional total variation[J].The Journal of Engineering,2013,2013(11):61-62.
[9]BAI J,FENG X C.Fractiona-order anisotropic diffusion for image denoising[J].IEEE Transactions on Image Processing,2007,16(10):2492-2502.
[10]ZHANG J P,CHEN K.A total fraction-order variation model for image restoration with non-honogeneous boundary conditions and its numerical solution[J].SIAM Journal on Imaging Science,2015,8(4):2487-2518.
[11]ARCHIBALD R,GELB A,PLATTE R.Image reconstruction from undersampled Fourier data using the polynomial annihilation transform[J].Journal of Scientific Computing,2016,67(2):432-452.
[12]GUO W H,QIN J,YIN W T.A new detail-preserving regularity scheme[J].SIAM Journal on Imaging Sciences,2014,7(2):1309-1334.
[13]WANG Q,WU Z H,SUN M J,et al.Single image super-resolution using directional total variation regularization and alternating direction method of multiplier solver[J].Journal of Electronic Imaging,2015,24(2):023026.
[14]CHAN T F,ESEDOGLU S.Aspects of total variation regularized L1function approximation[J].SIAM Journal on Applied Mathematics,2005,65(5):1817-1837.
[15]CHAMBOLLE A,POCK T.A first-order primal-dual algorithm for convex problems with applications to imaging[J].Journal of Mathematical Imaging and Vision,2011,40(1):120-145.
[16]YUAN J H,YANG J,SHI D,et al.A continuation fixed-point iterative method on harmonic generations with strong nonlinear optical effects in multi-layer structures[J].Computational and Applied Mathematics,2017,36(1):805-824.
[17]ECKSTEIN J,BERTSEKAS D.On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators[J].Mathematical Programming,1992,A55(3):293-318.
[18]XU Z B,ZENG J S,WANG Y,et al.L1/2regularization:Convergence of iterative half thresholding algorithm[J].IEEE Transactions on Signal Processing,2014,69(2):2317-2329.
[19]CHAN R,LIANG H X.Half-quadratic algorithm for eq-ep problems with application to TV-e1 image restoration and compressive sensing[M]∥BRUHN A,POCK T,TAI X C.Efficient algorithms for global optimization method in computer vision.Berlin:Springer,2014:78-103.