A non-negative quadratic programming approach to minimize the generalized vector-valued total variation functional

We propose a simple but flexible method for solving the generalized vector-valued TV (VTV) functional with a non-negativity constraint. One of the main features of this recursive algorithm is that it is based on multiplicative updates only and can be used to solve the denoising and deconvolution problems for vector-valued (color) images. This algorithm is the vectorial extension of the IRN-NQP (Iteratively Reweighted Norm - Non-negative Quadratic Programming) algorithm [1] originally developed for scalar (grayscale) images, and to the best of our knowledge, it is the only algorithm that explicitly includes a non-negativity constraint for color images within the TV framework.

[1]  Daniel D. Lee,et al.  Multiplicative Updates for Nonnegative Quadratic Programming , 2007, Neural Computation.

[2]  C. Vogel.  Computational Methods for Inverse Problems , 1987 .

[3]  J. Scales,et al.  Robust methods in inverse theory , 1988 .

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

[6]  Andy M. Yip,et al.  A Primal-Dual Active-Set Method for Non-Negativity Constrained Total Variation Deblurring Problems , 2007, IEEE Transactions on Image Processing.

[7]  J. Tukey,et al.  The Fitting of Power Series, Meaning Polynomials, Illustrated on Band-Spectroscopic Data , 1974 .

[8]  Michael K. Ng,et al.  Efficient Total Variation Minimization Methods for Color Image Restoration , 2008, IEEE Transactions on Image Processing.

[9]  Tony F. Chan,et al.  Total Variation Regularization of Matrix-Valued Images , 2007, Int. J. Biomed. Imaging.

[10]  Nahum Kiryati,et al.  Deblurring of Color Images Corrupted by Impulsive Noise , 2007, IEEE Transactions on Image Processing.

[11]  T. Brox,et al.  Diffusion and regularization of vector- and matrix-valued images , 2002 .

[12]  Brendt Wohlberg,et al.  Total-variation regularization with bound constraints , 2010, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing.

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

[14]  Paul Rodríguez.  Multiplicative updates algorithm to minimize the generalized total variation functional with a non-negativity constraint , 2010, 2010 IEEE International Conference on Image Processing.

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

[16]  Tony F. Chan,et al.  Total Variation Denoising and Enhancement of Color Images Based on the CB and HSV Color Models , 2001, J. Vis. Commun. Image Represent..

[17]  Rachid Deriche,et al.  Vector-valued image regularization with PDEs: a common framework for different applications , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[18]  Homer F. Walker,et al.  Choosing the Forcing Terms in an Inexact Newton Method , 1996, SIAM J. Sci. Comput..

[19]  Brendt Wohlberg,et al.  A generalized vector-valued total variation algorithm , 2009, 2009 16th IEEE International Conference on Image Processing (ICIP).

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

[21]  A. Bonnet,et al.  On the regularity of edges in image segmentation , 1996 .

[22]  Nikolas P. Galatsanos,et al.  Multichannel restoration of single channel images using a wavelet-based subband decomposition , 1994, IEEE Trans. Image Process..

[23]  Brendt Wohlberg,et al.  Efficient Minimization Method for a Generalized Total Variation Functional , 2009, IEEE Transactions on Image Processing.

[24]  R. Dembo,et al.  INEXACT NEWTON METHODS , 1982 .