Journal ArticleDOI
Past and future of inverse problems
TLDR
Inverse problems are those where a set of measured results is analyzed in order to get as much information as possible on a "model" which is proposed to represent a system in the real world as mentioned in this paper.Abstract:
Inverse problems are those where a set of measured results is analyzed in order to get as much information as possible on a “model” which is proposed to represent a system in the real world. Exact inverse problems are related to most parts of mathematics. Applied inverse problems are the keys to other sciences. Hence the field, which is very wealthy, yields the best example of interdisciplinary research but it has nevertheless a strong individuality. The obtained results and explored directions of the 20th century are sketched in this review, with attempts to predict their evolution.read more
Citations
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Journal ArticleDOI
Level set methods for inverse scattering
Oliver Dorn,Dominique Lesselier +1 more
TL;DR: In this paper, the authors give an overview of recent techniques which use a level set representation of shapes for solving inverse scattering problems, including shape sensitivity analysis and topological derivatives, and various techniques for incorporating regularization into the shape inverse problem using level sets.
Journal ArticleDOI
Contrast Source Inversion Method: State of Art
P.M. van den Berg,Aria Abubakar +1 more
TL;DR: Van den Berg and Abubakar as discussed by the authors discussed the possibility of the presence of local minima of the nonlinear cost functional and under which conditions they can exist, and introduced a new type of regularization, based on a weighted L 2 total variation norm.
Journal ArticleDOI
Inverse design in search of materials with target functionalities
TL;DR: In this article, a new style of collaboration between theory and experiment is discussed, whereby the desired functionality of the new material is declared first and theoretical calculations are then used to predict which stable and synthesizable compounds exhibit the required functionality.
Journal ArticleDOI
The Dreyfus model of clinical problem-solving skills acquisition: a critical perspective
TL;DR: Although the Dreyfus model may partially explain the ‘acquisition’ of some skills, it is debatable if it can explain the acquisition of clinical skills.
Journal ArticleDOI
Multiplicative regularization for contrast profile inversion
TL;DR: In this article, a new type of regularization technique for the nonlinear inverse scattering problem, namely the multiplicative technique, is discussed, which does not have to determine the regularization parameter before the inversion process is started.
References
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Book
Genetic algorithms in search, optimization, and machine learning
TL;DR: In this article, the authors present the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields, including computer programming and mathematics.
Genetic algorithms in search, optimization and machine learning
TL;DR: This book brings together the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields.
Book
Linear statistical inference and its applications
TL;DR: Algebra of Vectors and Matrices, Probability Theory, Tools and Techniques, and Continuous Probability Models.
Journal ArticleDOI
Linear Statistical Inference and its Applications
P. G. Moore,C. Radhakrishna Rao +1 more
TL;DR: The theory of least squares and analysis of variance has been studied in the literature for a long time, see as mentioned in this paper for a review of some of the most relevant works. But the main focus of this paper is on the analysis of variance.
Book
Inverse Acoustic and Electromagnetic Scattering Theory
David Colton,Rainer Kress +1 more
TL;DR: Inverse Medium Problem (IMP) as discussed by the authors is a generalization of the Helmholtz Equation for direct acoustical obstacle scattering in an Inhomogeneous Medium (IMM).