On the stability of inverse problems

By A. Tikhonov. 1943

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Citations in the corpus

Recent advances in convolutional neural networks (2015, background): “A more principled alternative of `2norm regularization is Tikhonov regularization [100], which rewards invariance to noise in the inputs.”
Processing of Structurally Heterogeneous Cryo-EM Data in RELION. (2016, methodology): “A commonly employed approach to similar questions in machine learning is known as Tikhonov regularization, where one restrains the square of the Euclidean (or L2) norm of the solution (Tikhonov, 1943).”
Deep learning generalizes because the parameter-function map is biased towards simple functions (2018, methodology): “Regarding 1), it was originally thought that regularization methods such as Tikhonov regularization (Tikhonov (1943)), dropout (Srivastava et al. (2014)), or early stopping (Morgan & Bourlard (1990)) were key in providing this inductive bias.”
Locally Weighted Ridge Regression for Power System Online Sensitivity Identification Considering Data Collinearity (2018, methodology): “Phillips invented the Tikhonov–Phillips regularization to solve the stability of inverse problems [8]–[10], and this algorithm was later applied in statistics by A.”
The stability for the Cauchy problem for elliptic equations (2009, background): “As is well-known since Tikhonov [95] the modern notion of stability for ill-posed problems (also called conditional stability) consists of estimating the dependence upon the data of the unknown solution of the problem at hand, when an a-priori bound on the solution itself is available.”