The statistical inverse problem of scatterometry: Bayesian inference and the effect of different priors

2015 ◽  
Author(s):  
Sebastian Heidenreich ◽  
Hermann Gross ◽  
Matthias Wurm ◽  
Bernd Bodermann ◽  
Markus Bär
Keyword(s):  
Inverse Problem ◽  
Bayesian Inference ◽  
Statistical Inverse Problem

A Statistical Inverse Problem Approach to Online Secondary Path Modeling in Active Noise Control

2016 ◽  
Vol 24 (1) ◽  
pp. 54-64 ◽  
Author(s):  
Iman Tabatabaei Ardekani ◽  
Jari P. Kaipio ◽  
Alireza Nasiri ◽  
Hamid Sharifzadeh ◽  
Waleed H. Abdulla
Keyword(s):  
Inverse Problem ◽  
Noise Control ◽  
Active Noise Control ◽  
Path Modeling ◽  
Active Noise ◽  
Statistical Inverse Problem ◽  
Secondary Path Modeling

From Non-Invasive Hemodynamic Measurements towards Patient-Specific Cardiovascular Diagnosis

2012 ◽  
pp. 1-25
Author(s):  
Stefan Bernhard ◽  
Kristine Al Zoukra ◽  
Christof Schtte
Keyword(s):  
Inverse Problem ◽  
Bayesian Inference ◽  
Cardiovascular Diseases ◽  
Cardiovascular System ◽  
Clinical Application ◽  
Patient Specific ◽  
The Novel ◽  
Physiological Models ◽  
Lack Of Information ◽  
Clinical Diagnoses

The past two decades have seen impressive success in medical technology, generating novel experimental data at an unexpected rate. However, current computational methods cannot sufficiently manage the data analysis for interpretation, so clinical application is hindered, and the benefit for the patient is still small. Even though numerous physiological models have been developed to describe complex dynamical mechanisms, their clinical application is limited, because parameterization is crucial, and most problems are ill-posed and do not have unique solutions. However, this information deficit is imminent to physiological data, because the measurement process always contains contamination like artifacts or noise and is limited by a finite measurement precision. The lack of information in hemodynamic data measured at the outlet of the left ventricle, for example, induces an infinite number of solutions to the hemodynamic inverse problem (possible vascular morphologies that can represent the hemodynamic conditions) (Quick, 2001). Within this work, we propose that, despite these problems, the assimilation of morphological constraints, and the usage of statistical prior knowledge from clinical observations, reveals diagnostically useful information. If the morphology of the vascular network, for example, is constrained by a set of time series measurements taken at specific places of the cardiovascular system, it is possible to solve the hemodynamic inverse problem by a carefully designed mathematical forward model in combination with a Bayesian inference technique. The proposed cardiovascular system identification procedure allows us to deduce patient-specific information that can be used to diagnose a variety of cardiovascular diseases in an early state. In contrast to traditional inversion approaches, the novel method produces a distribution of physiologically interpretable models (patient-specific parameters and model states) that allow the identification of disease specific patterns that correspond to clinical diagnoses, enabling a probabilistic assessment of human health condition on the basis of a broad patient population. In the ongoing work we use this technique to identify arterial stenosis and aneurisms from anomalous patterns in signal and parameter space. The novel data mining procedure provides useful clinical information about the location of vascular defects like aneurisms and stenosis. We conclude that the Bayesian inference approach is able to solve the cardiovascular inverse problem and to interpret clinical data to allow a patient-specific model-based diagnosis of cardiovascular diseases. We think that the information-based approach provides a useful link between mathematical physiology and clinical diagnoses and that it will become constituent in the medical decision process in near future.

From Non-Invasive Hemodynamic Measurements towards Patient-Specific Cardiovascular Diagnosis

Data Mining ◽  
2013 ◽  
pp. 2069-2093
Author(s):  
Stefan Bernhard ◽  
Kristine Al Zoukra ◽  
Christof Schtte
Keyword(s):  
Inverse Problem ◽  
Bayesian Inference ◽  
Cardiovascular Diseases ◽  
Cardiovascular System ◽  
Clinical Application ◽  
Patient Specific ◽  
The Novel ◽  
Physiological Models ◽  
Lack Of Information ◽  
Clinical Diagnoses

The past two decades have seen impressive success in medical technology, generating novel experimental data at an unexpected rate. However, current computational methods cannot sufficiently manage the data analysis for interpretation, so clinical application is hindered, and the benefit for the patient is still small. Even though numerous physiological models have been developed to describe complex dynamical mechanisms, their clinical application is limited, because parameterization is crucial, and most problems are ill-posed and do not have unique solutions. However, this information deficit is imminent to physiological data, because the measurement process always contains contamination like artifacts or noise and is limited by a finite measurement precision. The lack of information in hemodynamic data measured at the outlet of the left ventricle, for example, induces an infinite number of solutions to the hemodynamic inverse problem (possible vascular morphologies that can represent the hemodynamic conditions) (Quick, 2001). Within this work, we propose that, despite these problems, the assimilation of morphological constraints, and the usage of statistical prior knowledge from clinical observations, reveals diagnostically useful information. If the morphology of the vascular network, for example, is constrained by a set of time series measurements taken at specific places of the cardiovascular system, it is possible to solve the hemodynamic inverse problem by a carefully designed mathematical forward model in combination with a Bayesian inference technique. The proposed cardiovascular system identification procedure allows us to deduce patient-specific information that can be used to diagnose a variety of cardiovascular diseases in an early state. In contrast to traditional inversion approaches, the novel method produces a distribution of physiologically interpretable models (patient-specific parameters and model states) that allow the identification of disease specific patterns that correspond to clinical diagnoses, enabling a probabilistic assessment of human health condition on the basis of a broad patient population. In the ongoing work we use this technique to identify arterial stenosis and aneurisms from anomalous patterns in signal and parameter space. The novel data mining procedure provides useful clinical information about the location of vascular defects like aneurisms and stenosis. We conclude that the Bayesian inference approach is able to solve the cardiovascular inverse problem and to interpret clinical data to allow a patient-specific model-based diagnosis of cardiovascular diseases. We think that the information-based approach provides a useful link between mathematical physiology and clinical diagnoses and that it will become constituent in the medical decision process in near future.

scholarly journals Robust Multiscale Identification of Apparent Elastic Properties at Mesoscale for Random Heterogeneous Materials with Multiscale Field Measurements

Materials ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 2826 ◽  
Author(s):  
Tianyu Zhang ◽  
Florent Pled ◽  
Christophe Desceliers
Keyword(s):  
Inverse Problem ◽  
Stochastic Model ◽  
Elastic Properties ◽  
Plane Stress ◽  
Linear Elasticity ◽  
Field Measurements ◽  
Image Correlation ◽  
Stochastic Representation ◽  
Linear Elasticity Theory ◽  
Statistical Inverse Problem

The aim of this work is to efficiently and robustly solve the statistical inverse problem related to the identification of the elastic properties at both macroscopic and mesoscopic scales of heterogeneous anisotropic materials with a complex microstructure that usually cannot be properly described in terms of their mechanical constituents at microscale. Within the context of linear elasticity theory, the apparent elasticity tensor field at a given mesoscale is modeled by a prior non-Gaussian tensor-valued random field. A general methodology using multiscale displacement field measurements simultaneously made at both macroscale and mesoscale has been recently proposed for the identification the hyperparameters of such a prior stochastic model by solving a multiscale statistical inverse problem using a stochastic computational model and some information from displacement fields at both macroscale and mesoscale. This paper contributes to the improvement of the computational efficiency, accuracy and robustness of such a method by introducing (i) a mesoscopic numerical indicator related to the spatial correlation length(s) of kinematic fields, allowing the time-consuming global optimization algorithm (genetic algorithm) used in a previous work to be replaced with a more efficient algorithm and (ii) an ad hoc stochastic representation of the hyperparameters involved in the prior stochastic model in order to enhance both the robustness and the precision of the statistical inverse identification method. Finally, the proposed improved method is first validated on in silico materials within the framework of 2D plane stress and 3D linear elasticity (using multiscale simulated data obtained through numerical computations) and then exemplified on a real heterogeneous biological material (beef cortical bone) within the framework of 2D plane stress linear elasticity (using multiscale experimental data obtained through mechanical testing monitored by digital image correlation).

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