Parameter space study of optimal scale-dependent weights in TV image denoising

References

• Rudin LI, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms. Phys D: Nonlinear Phenomena. 1992;60(1–4):259–268.
   Web of Science ®Google Scholar
• Calatroni L, De Los Reyes JC, Schönlieb C-B. Infimal convolution of data discrepancies for mixed noise removal. SIAM J Imaging Sci. 2017;10(3):1196–1233.
   Web of Science ®Google Scholar
• Dong Y, Hintermüller M, Rincon-Camacho MM. Automated regularization parameter selection in multi-scale total variation models for image restoration. J Math Imaging Vis. 2011;40(1):82–104.
   Web of Science ®Google Scholar
• Hintermüller M, Rautenberg CN. Optimal selection of the regularization function in a weighted total variation model. part i: modelling and theory. J Math Imaging Vis. 2017;59(3):498–514.
   Web of Science ®Google Scholar
• Lauzier PT, Tang J, Chen G-H. Non-uniform noise spatial distribution in CT myocardial perfusion and a potential solution: statistical image reconstruction. In: SPIE medical imaging. San Diego (CA): International Society for Optics and Photonics; 2012. p. 831338.
   Google Scholar
• Lauzier PT, Tang J, Speidel MA, et al. Noise spatial nonuniformity and the impact of statistical image reconstruction in CT myocardial perfusion imaging. Med Phys. 2012;39(7):4079–4092.
   PubMed Web of Science ®Google Scholar
• De los Reyes JC, Schönlieb C-B. Image denoising: learning the noise model via nonsmooth pde-constrained optimization. Inverse Problems & Imaging. 2013;7(4):1183.
   Web of Science ®Google Scholar
• De los Reyes JC, Schönlieb C-B, Valkonen T. Bilevel parameter learning for higher-order total variation regularisation models. J Math Imaging Vis. 2017;57(1):1–25.
   PubMed Web of Science ®Google Scholar
• Gilboa G, Sochen NA, Zeevi YY. Estimation of optimal pde-based denoising in the snr sense. IEEE Trans Image Processing. 2006;15(8):2269–2280.
   PubMed Web of Science ®Google Scholar
• Strong DM, Aujol J-F, Chan TF. Scale recognition, regularization parameter selection, and meyer's g norm in total variation regularization. Multiscale Model Simul. 2006;5(1):273–303.
   Web of Science ®Google Scholar
• Van Chung C, De los Reyes JC, Schönlieb C-B. Learning optimal spatially-dependent regularization parameters in total variation image denoising. Inverse Probl. 2017;33(7):074005.
   Web of Science ®Google Scholar
• Wang Z, Simoncelli EP, Bovik AC. Multiscale structural similarity for image quality assessment. In: The 37th Asilomar Conference on Signals, Systems & Computers, 2003, Vol. 2. Pacific Grove (CA): IEEE; 2003. p. 1398–1402.
   Google Scholar
• De los Reyes JC, Schönlieb C-B, Valkonen T. The structure of optimal parameters for image restoration problems. J Math Anal Appl. 2016;434(1):464–500.
   Web of Science ®Google Scholar
• Bauschke HH, Combettes PL. Convex analysis and monotone operator theory in Hilbert spaces. Vol. 2011. New York (NY): Springer; 2017.
   Google Scholar
• Casas E. Boundary control of semilinear elliptic equations with pointwise state constraints. SIAM J Control Optim. 1993;31(4):993–1006.
   Web of Science ®Google Scholar
• Ito K, Kunisch K. Semi-smooth Newton methods for state-constrained optimal control problems. Syst Control Lett. 2003;50(3):221–228.
   Web of Science ®Google Scholar
• De los Reyes JC. Numerical PDE-constrained optimization. New York (NY): Springer; 2015.
   Google Scholar
• De los Reyes JC, Hintermüller M. A duality based semismooth newton framework for solving variational inequalities of the second kind. Interfaces Free Boundaries. 2011;13(4):437–462.
   Web of Science ®Google Scholar
• De los Reyes JC, Kunisch K. A semi-smooth newton method for control constrained boundary optimal control of the navier–stokes equations. Nonlinear Anal Theory, Methods Appl. 2005;62(7):1289–1316.
   Web of Science ®Google Scholar
• De los Reyes JC, Kunisch K. A semi-smooth newton method for regularized state-constrained optimal control of the navier-stokes equations. Computing. 2006;78(4):287–309.
   Web of Science ®Google Scholar
• Broyden CG, Dennis Jr JE, Moré JJ. On the local and superlinear convergence of quasi-newton methods. IMA J Appl Math. 1973;12(3):223–245.
   Google Scholar
• Calatroni L, Cao C, De los Reyes JC, et al. Bilevel approaches for learning of variational imaging models. In: Variational methods. Berlin (Germany): De Gruyter; 2016. p. 252–290.
   Google Scholar
• Martin D, Fowlkes C, Tal D, et al. A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. Vancouver (BC): Iccv Vancouver; 2001.
   Google Scholar
• Wang Z, Bovik AC, Sheikh HR, et al. Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process. 2004;13(4):600–612.
   PubMed Web of Science ®Google Scholar
• Bredies K, Dong Y, Hintermüller M. Spatially dependent regularization parameter selection in total generalized variation models for image restoration. Int J Comput Math. 2013;90(1):109–123.
   Web of Science ®Google Scholar
• Krasnoselskii MA, Zabreiko PP, Pustylii EL, et al. Integral operators in spaces of summable functions. Leyden (The Netherlands): Noordhoff International Publishing; 1976.
   Google Scholar
• Troianiello GM. Elliptic equations and obstacle problems. The University Series in Mathematics. Boston, MA: Springer; 1987.
   Google Scholar
• Gröger K. A W1,p-estimate for solutions to mixed boundary value problems for second order elliptic differential equations. Math Ann. 1989;283(4):679–687.
   Web of Science ®Google Scholar