A tensor voting based fractional-order image denoising model and its numerical algorithm

Abstract To take structure information into consideration, we propose a fractional-order image denoising model based on structure tensor. The existence and uniqueness of solution is proved. Furthermore, we also propose an alternating direction implicit (ADI) scheme of this model to find numerical solution and keep the stability of algorithm. Unconditional stability and convergence of this scheme is proved. Moreover, several numerical tests show that the proposed model can improve the denoising results of some published denoising models.

[1]  Dexing Kong,et al.  Salt and pepper noise removal based on an approximation of l0 norm , 2015, Comput. Math. Appl..

[2]  Huan Han.  A variational model with fractional-order regularization term arising in registration of diffusion tensor image , 2016, 1611.09202.

[3]  Xue-Cheng Tai,et al.  Noise removal using smoothed normals and surface fitting , 2004, IEEE Transactions on Image Processing.

[4]  YangQuan Chen,et al.  Fractional-order TV-L2 model for image denoising , 2013 .

[5]  Hong Wang,et al.  A superfast-preconditioned iterative method for steady-state space-fractional diffusion equations , 2013, J. Comput. Phys..

[6]  Yan Jin,et al.  A New Nonlocal H1 Model for Image Denoising , 2012, Journal of Mathematical Imaging and Vision.

[7]  Xiangyang Wang,et al.  An Efficient Remote Sensing Image Denoising Method in Extended Discrete Shearlet Domain , 2013, Journal of Mathematical Imaging and Vision.

[8]  Ke Chen,et al.  A Total Fractional-Order Variation Model for Image Restoration with Nonhomogeneous Boundary Conditions and Its Numerical Solution , 2015, SIAM J. Imaging Sci..

[9]  A. N. Tikhonov,et al.  Solutions of ill-posed problems , 1977 .

[10]  F. Demengel,et al.  Functional Spaces for the Theory of Elliptic Partial Differential Equations , 2012 .

[11]  Xue-Cheng Tai,et al.  Iterative Image Restoration Combining Total Variation Minimization and a Second-Order Functional , 2005, International Journal of Computer Vision.

[12]  Arvid Lundervold,et al.  Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time , 2003, IEEE Trans. Image Process..

[13]  Jie Huang,et al.  Speckle noise removal in ultrasound images by first- and second-order total variation , 2018, Numerical Algorithms.

[14]  Chengjian Zhang,et al.  A linear finite difference scheme for generalized time fractional Burgers equation , 2016 .

[15]  J. Weickert.  Applications of nonlinear diffusion in image processing and computer vision , 2000 .

[16]  Zhanqing Wang,et al.  An alternating direction implicit scheme of a fractional-order diffusion tensor image registration model , 2019, Appl. Math. Comput..

[17]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[18]  Xiaoping Yang,et al.  A Variational Model to Remove the Multiplicative Noise in Ultrasound Images , 2010, Journal of Mathematical Imaging and Vision.

[19]  Zhi-Zhong Sun,et al.  Error Analysis of a Compact ADI Scheme for the 2D Fractional Subdiffusion Equation , 2014, J. Sci. Comput..

[20]  Xiangchu Feng,et al.  Multiplicative noise removal using primal–dual and reweighted alternating minimization , 2016, SpringerPlus.

[21]  Dexing Kong,et al.  Nonlocal total variation models for multiplicative noise removal using split Bregman iteration , 2012, Math. Comput. Model..

[22]  Zhengmeng Jin,et al.  Analysis of a new variational model for multiplicative noise removal , 2010 .