Efficient Total Variation Minimization Methods for Color Image Restoration

In this paper, we consider and study a total variation minimization model for color image restoration. In the proposed model, we use the color total variation minimization scheme to denoise the deblurred color image. An alternating minimization algorithm is employed to solve the proposed total variation minimization problem. We show the convergence of the alternating minimization algorithm and demonstrate that the algorithm is very efficient. Our experimental results show that the quality of restored color images by the proposed method are competitive with the other tested methods.

[1]  Raymond H. Chan,et al.  A Fast Algorithm for Deblurring Models with Neumann Boundary Conditions , 1999, SIAM J. Sci. Comput..

[2]  Los Angeles,et al.  Dual Methods for Total Variation-Based Image , 2001 .

[3]  A. Banerjee.  Convex Analysis and Optimization , 2006 .

[4]  Michael K. Ng,et al.  Fast color image restoration with multisensors , 2002, Int. J. Imaging Syst. Technol..

[5]  Michael K. Ng,et al.  Structured Total Least Squares for Color Image Restoration , 2006, SIAM J. Sci. Comput..

[6]  Z. Opial.  Weak convergence of the sequence of successive approximations for nonexpansive mappings , 1967 .

[7]  B. R. Hunt,et al.  Karhunen-Loeve multispectral image restoration, part I: Theory , 1984 .

[8]  Nikolas P. Galatsanos,et al.  Digital restoration of multichannel images , 1989, IEEE Trans. Acoust. Speech Signal Process..

[9]  Nikolas P. Galatsanos,et al.  Least squares restoration of multichannel images , 1991, IEEE Trans. Signal Process..

[10]  M. Ng.  Iterative Methods for Toeplitz Systems , 2004 .

[11]  Nirmal K. Bose,et al.  Multispectral image restoration with multisensors , 1997, IEEE Trans. Geosci. Remote. Sens..

[12]  A. Wathen,et al.  Iterative Methods for Toeplitz Systems , 2005 .

[13]  Antonin Chambolle,et al.  A l1-Unified Variational Framework for Image Restoration , 2004, ECCV.

[14]  Curtis R. Vogel,et al.  Iterative Methods for Total Variation Denoising , 1996, SIAM J. Sci. Comput..

[15]  Patrick L. Combettes,et al.  Signal Recovery by Proximal Forward-Backward Splitting , 2005, Multiscale Model. Simul..

[16]  Michael K. Ng,et al.  On Semismooth Newton’s Methods for Total Variation Minimization , 2007, Journal of Mathematical Imaging and Vision.

[17]  Michael K. Ng,et al.  Comments on "Least squares restoration of multichannel images" , 2001, IEEE Trans. Signal Process..

[18]  Tony F. Chan,et al.  Color TV: total variation methods for restoration of vector-valued images , 1998, IEEE Trans. Image Process..

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

[20]  A. M. Tekalp,et al.  Multichannel image modeling and Kalman filtering for multispectral image restoration , 1990 .

[21]  M. Nikolova.  An Algorithm for Total Variation Minimization and Applications , 2004 .

[22]  D. Krishnan,et al.  An Efficient Operator-Splitting Method for Noise Removal in Images , 2006 .

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

[24]  T. Chan,et al.  Fast dual minimization of the vectorial total variation norm and applications to color image processing , 2008 .