scholarly journals Factorization method with one plane wave: from model-driven and data-driven perspectives

2021 ◽  
Author(s):  
Guanqiu Ma ◽  
Hu Guanghui
Keyword(s):  
A Priori ◽  
Plane Waves ◽  
Factorization Method ◽  
Data Driven ◽  
Field Pattern ◽  
Far Field ◽  
Model Driven ◽  
The One ◽  
Necessary And Sufficient ◽  
Mathematical Justification

Abstract The factorization method provides a necessary and sufficient condition for characterizing the shape and position of an unknown scatterer by using far-field patterns of infinitely many time-harmonic plane waves at a fixed frequency (which are also called the multistatic data response matrix). This paper is concerned with the factorization method with a single far-field pattern to recover an arbitrary convex polygonal scatterer/source. Its one-wave version relies on the absence of analytical continuation of the scattered/radiated wave-fields in corner domains. It can be regarded as a domain-defined sampling method and does not require forward solvers. In this paper we provide a rigorous mathematical justification of the one-wave factorization method and present some preliminary numerical examples. In particular, the proposed method can be interpreted as a model-driven and data-driven imaging scheme, and it shows how to incorporate a priori knowledge about the unknown target into the test scatterers for the purpose of detecting obstacles/sources with specific features.

scholarly journals Uniqueness in inverse electromagnetic scattering problem with phaseless far-field data at a fixed frequency

2020 ◽  
Author(s):  
Xiaoxu Xu ◽  
Bo Zhang ◽  
Haiwen Zhang
Keyword(s):  
Electromagnetic Scattering ◽  
Field Data ◽  
Scattering Problem ◽  
Plane Waves ◽  
Index Of Refraction ◽  
Field Pattern ◽  
Far Field ◽  
Fixed Frequency ◽  
Uniqueness Results ◽  
Far Field Pattern

Abstract This paper is concerned with uniqueness in inverse electromagnetic scattering with phaseless far-field pattern at a fixed frequency. In our previous work (2018,SIAM J. Appl. Math. 78, 3024–3039), by adding a known reference ball into the acoustic scattering system, it was proved that the impenetrable obstacle and the index of refraction of an inhomogeneous medium can be uniquely determined by the acoustic phaseless far-field patterns generated by infinitely many sets of superpositions of two plane waves with different directions at a fixed frequency. In this paper, we extend these uniqueness results to the inverse electromagnetic scattering case. The phaseless far-field data are the modulus of the tangential component in the orientations ${\boldsymbol{e}}_\phi $ and ${\boldsymbol{e}}_\theta $, respectively, of the electric far-field pattern measured on the unit sphere and generated by infinitely many sets of superpositions of two electromagnetic plane waves with different directions and polarizations. Our proof is mainly based on Rellich’s lemma and the Stratton–Chu formula for radiating solutions to the Maxwell equations.

Hybrid Newton-type methods for reconstructing sound-soft obstacles from a single far field

2016 ◽  
Vol 24 (1) ◽  
Author(s):  
Zewen Wang ◽  
Xiaoxia Li ◽  
Yun Xia
Keyword(s):  
Newton Method ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Field Pattern ◽  
Far Field ◽  
Newton Iterations ◽  
The One ◽  
Far Field Pattern ◽  
Quasi Newton ◽  
Multiple Obstacles

AbstractThe inverse scattering problem considered in this paper is to reconstruct multiple sound-soft obstacles from one incident wave and its far field pattern. Based on the ideas of the Kirsch–Kress method and the hybrid Newton method, three variant Newton-type methods are developed for reconstructing the shape of multiple obstacles. The proposed hybrid Newton-type methods I and II can choose auxiliary curves adaptively, and do not require them to be contained in the unknown multiple obstacles. The proposed hybrid Newton-type method III is simpler than the hybrid Newton method developed by Kress in terms of computational complexity since it adopts quasi-Newton iterations in numerical reconstructions. Results of numerical examples show that the proposed methods, especially the one with both adaptively choosing auxiliary curves and quasi-Newton iterations, are more efficient and stable for reconstructing multiple obstacles.

scholarly journals Model-Driven Interpretation in Intelligent Vision Systems

Perception ◽  
1976 ◽  
Vol 5 (3) ◽  
pp. 349-370 ◽  
Author(s):  
Alan K Mackworth
Keyword(s):  
A Priori ◽  
Scene Analysis ◽  
Adequate Account ◽  
Line Drawings ◽  
Model Driven ◽  
Knowledge Based ◽  
Psychological Theories ◽  
The One ◽  
Current Psychological ◽  
Use Of Models

With a constructive knowledge-based theory of perception as its foundation, this paper starts with a review and critique of some artificial-intelligence programs that purport to see. It is then argued that these computer programs for scene analysis offer the hope of providing a more adequate account of human competence in interpreting line drawings as polyhedra than do the current psychological theories. This thesis has several aspects. The one emphasized here is that those programs have explored a variety of methods of incorporating a priori knowledge of objects through the use of models. After outlining the range of models used, presenting a set of criteria for evaluating the use of model information, and sketching some psychological theories, the various proposals are contrasted. This discussion leads to two new proposals for exploiting model information that involve elaborations of an existing program, POLY.

Does Global Justice Require More than Just Global Institutions?

2016 ◽  
Vol 3 (1) ◽  
pp. 19-31
Author(s):  
Kok-Chor Tan
Keyword(s):  
Global Justice ◽  
The Other ◽  
Global Institutions ◽  
Institutional Approach ◽  
The One ◽  
Necessary And Sufficient ◽  
Strong Reading

The ‘institutional approach’ to justice holds that persons’ responsibility of justice is primarily to support, maintain, and comply with the rules of just institutions. Within the rules of just institutions, so long as their actions do not undermine these background institutions, individuals have no further responsibilities of justice. But what does the institutional approach say in the non-ideal context where just institutions are absent, such as in the global case? One reading of the institutional approach, in this case, is that our duties are primarily to create just institutions, and that when we are doing our part in this respect, we may legitimately pursue other personal or associational ends. This ‘strong’ reading of our institutional duty takes it to be both a necessary and sufficient duty of justice of individuals that they do their part to establish just arrangements. But how plausible is this? On the one hand this requirement seems overly inflexible; on the other it seems overly lax. I clarify the motivation and context of this reading of the institutional duty, and suggest that it need not be as implausible as it seems.

scholarly journals Incorporating radiomics into clinical trials: expert consensus on considerations for data-driven compared to biologically driven quantitative biomarkers

2021 ◽  
Author(s):  
Laure Fournier ◽  
Lena Costaridou ◽  
Luc Bidaut ◽  
Nicolas Michoux ◽  
Frederic E. Lecouvet ◽  
...  
Keyword(s):  
Clinical Trials ◽  
Quantitative Imaging ◽  
A Priori ◽  
External Validation ◽  
Data Driven ◽  
Imaging Biomarkers ◽  
Clinical Validation ◽  
Biological Processes ◽  
Imaging Data ◽  
Selection Of

Abstract Existing quantitative imaging biomarkers (QIBs) are associated with known biological tissue characteristics and follow a well-understood path of technical, biological and clinical validation before incorporation into clinical trials. In radiomics, novel data-driven processes extract numerous visually imperceptible statistical features from the imaging data with no a priori assumptions on their correlation with biological processes. The selection of relevant features (radiomic signature) and incorporation into clinical trials therefore requires additional considerations to ensure meaningful imaging endpoints. Also, the number of radiomic features tested means that power calculations would result in sample sizes impossible to achieve within clinical trials. This article examines how the process of standardising and validating data-driven imaging biomarkers differs from those based on biological associations. Radiomic signatures are best developed initially on datasets that represent diversity of acquisition protocols as well as diversity of disease and of normal findings, rather than within clinical trials with standardised and optimised protocols as this would risk the selection of radiomic features being linked to the imaging process rather than the pathology. Normalisation through discretisation and feature harmonisation are essential pre-processing steps. Biological correlation may be performed after the technical and clinical validity of a radiomic signature is established, but is not mandatory. Feature selection may be part of discovery within a radiomics-specific trial or represent exploratory endpoints within an established trial; a previously validated radiomic signature may even be used as a primary/secondary endpoint, particularly if associations are demonstrated with specific biological processes and pathways being targeted within clinical trials. Key Points • Data-driven processes like radiomics risk false discoveries due to high-dimensionality of the dataset compared to sample size, making adequate diversity of the data, cross-validation and external validation essential to mitigate the risks of spurious associations and overfitting. • Use of radiomic signatures within clinical trials requires multistep standardisation of image acquisition, image analysis and data mining processes. • Biological correlation may be established after clinical validation but is not mandatory.

scholarly journals The New Trend of State Estimation: From Model-Driven to Hybrid-Driven Methods

Sensors ◽  
2021 ◽  
Vol 21 (6) ◽  
pp. 2085
Author(s):  
Xue-Bo Jin ◽  
Ruben Jonhson Robert RobertJeremiah ◽  
Ting-Li Su ◽  
Yu-Ting Bai ◽  
Jian-Lei Kong
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Future Development ◽  
Data Driven ◽  
Estimation Methods ◽  
Multiple Model ◽  
Development Trends ◽  
Research Results ◽  
Model Driven ◽  
Model Based

State estimation is widely used in various automated systems, including IoT systems, unmanned systems, robots, etc. In traditional state estimation, measurement data are instantaneous and processed in real time. With modern systems’ development, sensors can obtain more and more signals and store them. Therefore, how to use these measurement big data to improve the performance of state estimation has become a hot research issue in this field. This paper reviews the development of state estimation and future development trends. First, we review the model-based state estimation methods, including the Kalman filter, such as the extended Kalman filter (EKF), unscented Kalman filter (UKF), cubature Kalman filter (CKF), etc. Particle filters and Gaussian mixture filters that can handle mixed Gaussian noise are discussed, too. These methods have high requirements for models, while it is not easy to obtain accurate system models in practice. The emergence of robust filters, the interacting multiple model (IMM), and adaptive filters are also mentioned here. Secondly, the current research status of data-driven state estimation methods is introduced based on network learning. Finally, the main research results for hybrid filters obtained in recent years are summarized and discussed, which combine model-based methods and data-driven methods. This paper is based on state estimation research results and provides a more detailed overview of model-driven, data-driven, and hybrid-driven approaches. The main algorithm of each method is provided so that beginners can have a clearer understanding. Additionally, it discusses the future development trends for researchers in state estimation.

scholarly journals Minkowski box from Yangian bootstrap

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Luke Corcoran ◽  
Florian Loebbert ◽  
Julian Miczajka ◽  
Matthias Staudacher
Keyword(s):  
Minkowski Space ◽  
Wigner Function ◽  
Functional Form ◽  
A Priori ◽  
Alternative Methods ◽  
Feynman Integrals ◽  
The One

Abstract We extend the recently developed Yangian bootstrap for Feynman integrals to Minkowski space, focusing on the case of the one-loop box integral. The space of Yangian invariants is spanned by the Bloch-Wigner function and its discontinuities. Using only input from symmetries, we constrain the functional form of the box integral in all 64 kinematic regions up to twelve (out of a priori 256) undetermined constants. These need to be fixed by other means. We do this explicitly, employing two alternative methods. This results in a novel compact formula for the box integral valid in all kinematic regions of Minkowski space.

The inverse elastic scattering by an impenetrable obstacle and a crack

2020 ◽  
Author(s):  
Jianli Xiang ◽  
Guozheng Yan
Keyword(s):  
Mixed Type ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Field Operator ◽  
Integral Equation Method ◽  
Factorization Method ◽  
Boundary Integral ◽  
Far Field ◽  
Direct Scattering ◽  
Time Harmonic

Abstract This paper is concerned with the inverse scattering problem of time-harmonic elastic waves by a mixed-type scatterer, which is given as the union of an impenetrable obstacle and a crack. We develop the modified factorization method to determine the shape of the mixed-type scatterer from the far field data. However, the factorization of the far field operator $F$ is related to the boundary integral matrix operator $A$, which is obtained in the study of the direct scattering problem. So, in the first part, we show the well posedness of the direct scattering problem by the boundary integral equation method. Some numerical examples are presented at the end of the paper to demonstrate the feasibility and effectiveness of the inverse algorithm.

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