A Generalized Vector-Valued Total Variation Algorithm

Total Variation algorithm for denoising/deconvolving grayscale/color (vector) images

Compute the minimum of the generalized TV functional
T = F( K*U - S ) + lambda*|| sqrt( (Dx(U))^2 + (Dy(U))^2 ) ||^q

for grayscale / color (vector) images using the IRN [1-9] algorithm, where

F: function that describes the noise model (Gaussian, Salt & Pepper, Poisson, Gamma, mixed
Gaussian/S&P and mixed Gaussian/Random models supported).
S: Input image
lambda: regularization parameter
K: linear operator
U: Output image

References

[1] P. Rodriguez, B. Wohlberg, "Efficient Minimization Method for a Generalized Total Variation Functional"
IEEE Transactions on Image Processing, 2009, 18:2(322-332)

[2] P. Rodríguez, B. Wohlberg "A Generalized Vector-Valued Total Variation Algorithm", in Proceedings of the IEEE International Conference on Image Processing (ICIP), (Cairo, Egypt), doi:10.1109/ICIP.2009.5413587, pp 1309--1312, Nov. 2009.

[3] P. Rodríguez, "Multiplicative Updates Algorithm to Minimize the Generalized Total Variation Functional with a Non-negativity Constraint", Proceedings of the IEEE International Conference on Image Processing (ICIP), (Hong Kong), doi:10.1109/ICIP.2010.5654074, pp 2509--2512, September, 2010

[4] Paul Rodríguez, "A Non-negative Quadratic Programming approach to Minimize the Generalized Vector-Valued Total Variation Functional", Proceedings of the European Signal Processing Conference (EUSIPCO), (Aalborg, Denmark), pp. 314--318, August, 2010.

[5] P. Rodríguez, "NonConvex Total Variation Speckled Image Restoration via Nonnegative Quadratic Programming Algorithm", Proceedings of the European Signal Processing Conference (EUSIPCO), (Barcelona, Spain), pp. 288-292, August, 2011.

[6] R. Rojas, P. Rodríguez, "Spatially Adaptive Total Variation Image Denoising Under Salt And Pepper Noise", Proceedings of the European Signal Processing Conference (EUSIPCO), (Barcelona, Spain), pp 278-282, August, 2011.

[7] P. Rodríguez, "Total Variation Regularization for Poisson Vector-Valued Image Restoration with a Spatially Adaptive Regularization Parameter Selection", Proceedings of the IEEE Symposium on Image and Signal Processing and Analysis (ISPA), (Dubrovnik, Croatia), pp. 402-407, September, 2011.

[8] P. Rodríguez, R. Rojas, B. Wohlberg, "Mixed Gaussian-Impulse Noise Image Restoration via Total Variation", IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), (Kyoto, Japan), doi: 10.1109/ICASSP.2012.6288073, pp. 1077--1080, March, 2012

[9] P. Rodríguez, B. Wohlberg, "Performance Comparison of Iterative Reweighting Methods for Total Variation Regularization", accepted IEEE International Conference on Image Processing (ICIP), (Paris, France), October, 2014.