Abstract
In this paper, we present a new version of the famous Rudin-Osher-Fatemi (ROF) model to restore image. The key point of the model is that it could reconstruct images with blur and non-uniformly distributed noise. We develop this approach by adding several statistical control parameters to the cost functional, and these parameters could be adaptively determined by the given observed image. In this way, we could adaptively balance the performance of the fit-to-data term and the regularization term. The Numerical experiments have demonstrated the significant effectiveness and robustness of our model in restoring blurred images with mixed Gaussian noise or salt-and-pepper noise.
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References
Acar, R., & Vogel, C. (1994). Analysis of total variation penalty methods. Inverse Problems, 10, 1217–1229.
Bar, L., Kiryati, N., & Sochen, N. (2006). Image deblurring in the presence of impulsive noise. International Journal of Computer Vision, 70, 279–298.
Bect, J., Blanc-Féraud, L., Aubert, J., & Chambolle, A. (2004). A l 1-unified variational framework for image restoration. In Proc. ECCV’2004, Prague, Czech Republic, Part IV: LNCS 3024 (pp. 1–13).
Bilmes, J. (1998). A gentle tutorial of the EM algorithm and its application to parameter estimation for Gaussian mixture and hidden Markov models. Available at http://citeseer.ist.psu.edu/bilmes98gentle.html.
Chan, T., & Wong, C. (1998). Total variation blind deconvolution. IEEE Trans. Image Processing, 7, 370–375.
Chan, R., Ho, C., & Nikolova, M. (2005). Salt-and-pepper noise removal by median-type noise detectors and detail-preserving regularization. IEEE Transactions on Image Processing, 14(10), 1479–1485.
He, L., Marquina, A., & Osher, J. (2005). Blind Deconvolution Using TV Regularization and Bregman Iteration. International Journal of Imaging Systems Technology, 15, 74–83.
Lagendijk, R., & Biemond, J. (1988). Regularized iterative image restoration with ringing reduction. IEEE Transaction on Acoustics, Speech, and Signal Processing, 36(12), 1874–1888.
McLachlan, G., & Krishnan, H. (1997). The EM algorithm and extensions. New York: Wiley.
Michael, K., Chan, H., & Tang, W. (1999). A fast algorithm for deblurring models with Neumann boundary conditions. SIAM Journal of Scientific Computation, 21(3), 851–866.
Nikolova, M. (2004). A variational approach to remove outliers and impulse noise. Journal of Mathematical Imaging and Vision, 20, 99–120.
Redner, R., & Walker, H. (1984). Mixture densities maximum likelihood and the EM algorithm. SIAM Review, 26(2), 195–239.
Rudin, L., & Osher, S. (1994). Total variation based image restoration with free local constraints. In Proc. IEEE ICIP (Vol. 1, pp. 31–35) Austin TX, USA.
Rudin, L., Osher, S., & Fatemi, E. (1992). Nonlinear total variation based noise removal algorithms. Journal of Physics D, 60, 259–268.
Shi, Y., & Chang, Q. (2006). New time dependent model for image restoration. Applied Mathematics and Computation, 179(1), 121–134.
Shi, Y., & Chang, Q. (2007). Acceleration methods for image restoration problem with different boundary conditions. Applied Numerical Mathematics, 58(5), 602–614.
Vogel, R. (2002). Computational methods for inverse problems. SIAM.
Vogel, C., & Oman, M. (1998). Fast, robust total variation-based reconstruction of noisy, blurred images. IEEE Transactions on Image Processing, 7, 813–824.
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Liu, J., Huan, Z., Huang, H. et al. An Adaptive Method for Recovering Image from Mixed Noisy Data. Int J Comput Vis 85, 182–191 (2009). https://doi.org/10.1007/s11263-009-0254-9
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DOI: https://doi.org/10.1007/s11263-009-0254-9