Consistency and rates of convergence of nonlinear Tikhonov regularization with random noise

By Nicolai Bissantz, Thorsten Hohage, Axel Munk. 2004

87 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Electrical and Electronic Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fec8a57adf3ef3c0fa2b4d297c08e2e7b0ac9964

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

1. Kim Knudsen
2. Samuli Siltanen
3. Jennifer L. Mueller
4. X. d'Haultfoeuille
5. Martin Burger
6. Matti Lassas
7. Martin Benning
8. Peter Maass

In Electrical and Electronic Engineering

1. Kim Knudsen
2. Matti Lassas
3. Jennifer L. Mueller
4. Samuli Siltanen
5. X. d'Haultfoeuille
6. Martin Burger
7. Joel L. Horowitz
8. Andreas Hauptmann

In Mathematical Physics

1. X. d'Haultfoeuille
2. S. Lee
3. Kim Knudsen
4. Matti Lassas
5. Samuli Siltanen
6. Jennifer L. Mueller
7. Joel L. Horowitz
8. Martin Benning

Citations in the corpus

• A New Instrumental Method for Dealing with Endogenous Selection (2010, methodology): “This and the fact that DM is weakly closed ensures that T is weakly sequentially closed (see Bissantz et al., 2004). Consequently, we can apply the end of the proof of Theorem 2 of Bissantz et al. (2004), and the result follows”
• Nonparametric Instrumental Variables Estimation of a Quantile Regression Model (2006, background): “6.1 Proof of Theorem 1 The proof is a modification of the proof of Theorem 2 of Bissantz, Hohage, and Munk (2004).”
• Nonparametric statistical inverse problems (2008, background): “Some recent papers concerning nonlinear inverse problems are [4, 45].”
• Discretization-invariant Bayesian inversion and Besov space priors (2009, unknown): “For regularization based approaches for statistical inverse problems, see [9, 25, 26, 54].”
• Modern regularization methods for inverse problems (2018, background): “range of the forward operator K. 4.3 Stochastic Approaches In addition to the deterministic viewpoint a statistical approach has become popular also in innite-dimensional problems more recently (cf. [41, 42, 107, 238, 188, 220]). In such a setup the data f are considered to be random variables drawn”
• REGULARIZED D-BAR METHOD FOR THE INVERSE CONDUCTIVITY PROBLEM (2009, background): “Iterative regularization of both linear and nonlinear inverse problems and convergence rates are discussed in Hilbert space setting in [9, 33, 35, 65, 66] and in Banach space setting in [34, 44, 45, 48, 76, 77, 78].”