Variational Methods in Imaging

By Otmar Scherzer, Markus Grasmair, H. Grossauer, Markus Haltmeier, Frank Lenzen. Applied Mathematical Sciences, 2008

602 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/0b47a063fb29d2688226a289b84120661fcdc216

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In Biomedical Engineering

In Radiology, Nuclear Medicine and Imaging

Citations in the corpus

Infimal convolution regularizations with discrete ℓ1-type functionals (2011, background): “For other generalizations of TV we refer to [31].”
Regularization properties of the sequential discrepancy principle for Tikhonov regularization in Banach spaces (2014, background): “[5,8,9]), and summarize some mathematical consequences of those standard assumptions.”
On the interplay of source conditions and variational inequalities for nonlinear ill-posed problems (2010, background): “38 in [1] which just handle the case 1⁄4 1.”
Total Generalized Variation (2010, methodology): “For various other aspects on the topic of constructing appropriate regularization or filter functionals in image reconstruction, we refer the reader to [SGGHL] and the references given there.”
Deep Neural Networks Motivated by Partial Differential Equations (2018, methodology): “ying functions. This continuous data model has led to solid mathematical theories for classical data processing tasks obtained by leveraging the rich results from PDEs and variational calculus (e.g., [38]). The continuous perspective has also enabled more abstract formulations that are independent o”
Solving inverse problems using data-driven models (2019, methodology): “The idea here is to minimize a measure of data misfit that is penalized using a regularizer (Kaltenbacher, Neubauer and Scherzer 2008, Scherzer et al. 2009): Rθ(g) := arg min f∈X {L(A(f), g) + Sθ(f)}, (2.7) where we make use of the notation in Definitions 2.2, 2.4 and 2.5.”
NETT: solving inverse problems with deep neural networks (2018, background): “For convex regularizers, the notion of Bregman distance is a powerful concept [8, 44].”
An extension of the variational inequality approach for obtaining convergence rates in regularization of nonlinear ill-posed problems (2010, background): “In recent publications (see [12, 13, 16, 25]) variational inequalities of the form”
Sparse regularization with lq penalty term (2008, methodology): “Requiring differentiability of uα , he used the square of a higher order weighted Sobolev norm as a penalty term [26, 27].”