Bilevel approaches for learning of variational imaging models

Calatroni, Luca; Chung, Cao Van; Reyes, Juan C.; Schönlieb, Carola‐Bibiane; Valkonen, Tuomo

doi:10.48550/arxiv.1505.02120

Cited by 6 publications

(9 citation statements)

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“…Recently established concepts of bilevel optimisation and parameter learning for variational imaging models (cf. [37,38]) might supplement our framework.…”

Section: Mitosisanalyser Frameworkmentioning

confidence: 96%

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Mathematical imaging methods for mitosis analysis in live-cell phase contrast microscopy

Grah

Harrington

Koh

et al. 2017

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In this paper we propose a workflow to detect and track mitotic cells in time-lapse microscopy image sequences. In order to avoid the requirement for cell lines expressing fluorescent markers and the associated phototoxicity, phase contrast microscopy is often preferred over fluorescence microscopy in live-cell imaging. However, common specific image characteristics complicate image processing and impede use of standard methods. Nevertheless, automated analysis is desirable due to manual analysis being subjective, biased and extremely time-consuming for large data sets. Here, we present the following workflow based on mathematical imaging methods. In the first step, mitosis detection is performed by means of the circular Hough transform. The obtained circular contour subsequently serves as an initialisation for the tracking algorithm based on variational methods. It is sub-divided into two parts: in order to determine the beginning of the whole mitosis cycle, a backwards tracking procedure is performed. After that, the cell is tracked forwards in time until the end of mitosis. As a result, the average of mitosis duration and ratios of different cell fates (cell death, no division, division into two or more daughter cells) can be measured and statistics on cell morphologies can be obtained. All of the tools are featured in the user-friendly MATLAB®Graphical User Interface MitosisAnalyser.

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“…Recently established concepts of bilevel optimisation and parameter learning for variational imaging models (cf. [37,38]) might supplement our framework.…”

Section: Mitosisanalyser Frameworkmentioning

confidence: 96%

“…Consequently, this may in turn lead to enhancement of image processing. Recently established concepts of bilevel optimisation and parameter learning for variational imaging models (cf [37,38]…”

mentioning

confidence: 99%

Mathematical imaging methods for mitosis analysis in live-cell phase contrast microscopy

Grah

Harrington

Koh

et al. 2017

Methods

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“…This was first developed for hyperparameter optimization in neural networks (Larsen et al, 1996) and developed further by Pedregosa (2016). Similar approaches have been used for hyperparameter optimization in log-linear models (Foo et al, 2008), kernel selection (Chapelle et al, 2002;Seeger, 2007), and image reconstruction (Kunisch & Pock, 2013;Calatroni et al, 2015). Both approaches struggle with certain hyperparameters, since they differentiate gradient descent or the training loss with respect to the hyperparameters.…”

Section: Related Workmentioning

confidence: 99%

Self-Tuning Networks: Bilevel Optimization of Hyperparameters using Structured Best-Response Functions

MacKay,

Vicol,

Lorraine

et al. 2019

Preprint

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Hyperparameter optimization can be formulated as a bilevel optimization problem, where the optimal parameters on the training set depend on the hyperparameters. We aim to adapt regularization hyperparameters for neural networks by fitting compact approximations to the best-response function, which maps hyperparameters to optimal weights and biases. We show how to construct scalable best-response approximations for neural networks by modeling the best-response as a single network whose hidden units are gated conditionally on the regularizer. We justify this approximation by showing the exact best-response for a shallow linear network with L 2 -regularized Jacobian can be represented by a similar gating mechanism. We fit this model using a gradient-based hyperparameter optimization algorithm which alternates between approximating the best-response around the current hyperparameters and optimizing the hyperparameters using the approximate best-response function. Unlike other gradient-based approaches, we do not require differentiating the training loss with respect to the hyperparameters, allowing us to tune discrete hyperparameters, data augmentation hyperparameters, and dropout probabilities. Because the hyperparameters are adapted online, our approach discovers hyperparameter schedules that can outperform fixed hyperparameter values. Empirically, our approach outperforms competing hyperparameter optimization methods on large-scale deep learning problems. We call our networks, which update their own hyperparameters online during training, Self-Tuning Networks (STNs). * Equal contribution. 1 The uniqueness of the arg min is assumed.

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“…Once the parameters in the variational model are learned on the basis of the training set, then the learned model is used for new image data. See [2] for a recent review on bilevel learning in image processing.…”

Section: The Bilevel Optimization Problem In Function Spacementioning

confidence: 99%

“…We have outlined the reason for the Huber regularization above. The reason for the addition of the elliptic term µ Du 2 2 to (1.1) is, that it numerically renders the inversion of the Hessian of the lower level functional more robust and that it places the problem in Hilbert space and therefore opens up a large toolbox for the analysis of the smoothed problem and its approximation properties, see also [8].…”

Section: The Bilevel Optimization Problem In Function Spacementioning

confidence: 99%

Learning optimal spatially-dependent regularization parameters in total variation image denoising

2017

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We consider a bilevel optimization approach in function space for the choice of spatially dependent regularization parameters in TV image denoising models. First-and second-order optimality conditions for the bilevel problem are studied when the spatiallydependent parameter belongs to the Sobolev space H 1 (Ω). A combined Schwarz domain decomposition-semismooth Newton method is proposed for the solution of the full optimality system and local superlinear convergence of the semismooth Newton method is verified. Exhaustive numerical computations are finally carried out to show the suitability of the approach.2010 Mathematics Subject Classification. 47N40, 65D18, 65N06, 68W10, 65M55.

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Bilevel approaches for learning of variational imaging models

Cited by 6 publications

References 0 publications

Mathematical imaging methods for mitosis analysis in live-cell phase contrast microscopy

Mathematical imaging methods for mitosis analysis in live-cell phase contrast microscopy

Self-Tuning Networks: Bilevel Optimization of Hyperparameters using Structured Best-Response Functions

Learning optimal spatially-dependent regularization parameters in total variation image denoising

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