Trainable Regularization for Multi-frame Superresolution

Klatzer, Teresa; Soukup, Daniel; Kobler, Erich; Hammernik, Kerstin; Pock, Thomas

doi:10.1007/978-3-319-66709-6_8

Cited by 4 publications

(6 citation statements)

References 12 publications

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“…bilevel learning for image segmentation (Ranftl and Pock 2014)) as well as classification ( e.g. learning an optimal set-up of support vector machines (Klatzer and Pock 2015)).…”

Section: Learning In Functional Analytic Regularizationmentioning

confidence: 99%

Solving inverse problems using data-driven models

et al. 2019

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Recent research in inverse problems seeks to develop a mathematically coherent foundation for combining data-driven models, and in particular those based on deep learning, with domain-specific knowledge contained in physical–analytical models. The focus is on solving ill-posed inverse problems that are at the core of many challenging applications in the natural sciences, medicine and life sciences, as well as in engineering and industrial applications. This survey paper aims to give an account of some of the main contributions in data-driven inverse problems.

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“…bilevel learning for image segmentation (Ranftl and Pock 2014)) as well as classification ( e.g. learning an optimal set-up of support vector machines (Klatzer and Pock 2015)).…”

Section: Learning In Functional Analytic Regularizationmentioning

confidence: 99%

Solving inverse problems using data-driven models

et al. 2019

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“…Finally, we are aware of deep learning techniques for superresolution, see, e.g. [13,25]. We will consider such approaches in the future which would also benefit from dimensionality reduction, in particular in 3D.…”

Section: Discussionmentioning

confidence: 99%

“…Proof. For fixed U and b, we have as in the classical GMM, see (2), that the maximizer in (13) with respect to µ and Σ fulfills…”

Section: End Formentioning

confidence: 99%

PCA Reduced Gaussian Mixture Models with Applications in Superresolution

Hertrich,

Nguyen,

Aujol

et al. 2020

Preprint

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Despite the rapid development of computational hardware, the treatment of large and high dimensional data sets is still a challenging problem. This paper provides a twofold contribution to the topic. First, we propose a Gaussian Mixture Model in conjunction with a reduction of the dimensionality of the data in each component of the model by principal component analysis, called PCA-GMM. To learn the (low dimensional) parameters of the mixture model we propose an EM algorithm whose M-step requires the solution of constrained optimization problems. Fortunately, these constrained problems do not depend on the usually large number of samples and can be solved efficiently by an (inertial) proximal alternating linearized minimization algorithm. Second, we apply our PCA-GMM for the superresolution of 2D and 3D material images based on the approach of Sandeep and Jacob. Numerical results confirm the moderate influence of the dimensionality reduction on the overall superresolution result.

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“…2017, Kobler, Klatzer, Hammernik and Pock 2017, Klatzer et al. 2017), and other works related to image processing (Ochs, Ranftl, Brox and Pock 2015, Hintermüller and Wu 2015).…”

Section: Advanced Issuesmentioning

confidence: 99%

Modern regularization methods for inverse problems

2018

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Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from linear towards nonlinear regularization methods even for linear inverse problems. The aim of this paper is to provide a reasonably comprehensive overview of this development towards modern nonlinear regularization methods, including their analysis, applications, and issues for future research.In particular we will discuss variational methods and techniques derived from those, since they have attracted particular interest in the last years and link to other fields like image processing and compressed sensing. We further point to developments related to statistical inverse problems, multiscale decompositions, and learning theory.

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Trainable Regularization for Multi-frame Superresolution

Cited by 4 publications

References 12 publications

Solving inverse problems using data-driven models

Solving inverse problems using data-driven models

PCA Reduced Gaussian Mixture Models with Applications in Superresolution

Modern regularization methods for inverse problems

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