Casting inverse
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Casting inverse
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Discover more about: Inverse Problems
: In this paper we study the existence of C 2;ff domain solutions for a class of free boundary problems which are critical domains for a shape functional depending on a general term (in most PDE applications this term represents the energy associated) and the perimeter, under the constraint that the measure ofOmega is given. As an application there are considered two problems. They involve ... [Show full abstract] respectively the Dirichlet problem inOmega ae R N and the exterior electromagnetic casting problem in R 3 . Mathematics Subject Classification (1991): 62K05; 49K30 1 Introduction In this paper we present a sufficient condition for the existence of C 2;ff critical domains of a shape functional E(OmegaGamma = e(OmegaGamma + 1 oe 2 P(OmegaGamma9 whereOmega ae R N is a C 2;ff open set, e(OmegaGamma is a shape functional satisfying some hypothesis given later, P(OmegaGamma is the perimeter ofOmega and oe 2 R, under the constraint that the measure m(OmegaGamma ofOmega ...
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9 May 2022
·
Ivan Ezhov ,
Marcel Rosier ,
Lucas Zimmer ,
Florian Kofler ,
Suprosanna Shit ,
Johannes Paetzold ,
Kevin Scibilia ,
Leon Maechler ,
Katharina Franitza ,
Tamaz Amiranashvili ,
Martin J. Menten ,
Marie Metz ,
Sailesh Conjeti ,
Benedikt Wiestler ,
Bjoern Menze
·
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Solving the inverse problem is the key step in evaluating the capacity of a physical model to describe real phenomena. In medical image computing, it aligns with the classical theme of image-based model personalization. Traditionally, a solution to the problem is obtained by performing either sampling or variational inference based methods. Both approaches aim to identify a set of free physical model parameters that results in a simulation best matching an empirical observation. When applied to brain tumor modeling, one of the instances of image-based model personalization in medical image computing, the overarching drawback of the methods is the time complexity for finding such a set. In a clinical setting with limited time between imaging and diagnosis or even intervention, this time complexity may prove critical. As the history of quantitative science is the history of compression, we align in this paper with the historical tendency and propose a method compressing complex traditional strategies for solving an inverse problem into a simple database query task. We evaluated different ways of performing the database query task assessing the trade-off between accuracy and execution time. On the exemplary task of brain tumor growth modeling, we prove that the proposed method achieves one order speed-up compared to existing approaches for solving the inverse problem. The resulting compute time offers critical means for relying on more complex and, hence, realistic models, for integrating image preprocessing and inverse modeling even deeper, or for implementing the current model into a clinical workflow.
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