Estimating the periodic components of a biomedical signal through inverse problem modelling and Bayesian inference with sparsity enforcing prior

2015 ◽  
Author(s):  
Mircea Dumitru ◽  
Ali-Mohammad Djafari
Keyword(s):  
Inverse Problem ◽  
Bayesian Inference ◽  
Biomedical Signal ◽  
Periodic Components

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 Bayesian inference applied to the electromagnetic inverse problem

1999 ◽  
Vol 7 (3) ◽  
pp. 195-212 ◽  
Author(s):  
David M. Schmidt ◽  
John S. George ◽  
C.C. Wood
Keyword(s):  
Inverse Problem ◽  
Bayesian Inference

scholarly journals Bayesian inference and Markov chain Monte Carlo based estimation of critical slip distance parameter in rate and state model for fault friction

2021 ◽  
Author(s):  
Saumik Dana
Keyword(s):  
Inverse Problem ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Inference ◽  
State Model ◽  
Seismogenic Fault ◽  
Fault Friction ◽  
Distance Parameter ◽  
Slip Distance

We present an algorithmic framework to solve an inverse problem using Bayesian inference and Markov chain Monte Carlo sampling. The input of the inverse problem is the acceleration of the slipping seismogenic fault and the output is the probability distribution of the critical slip distance parameter of the rate and state model for fault friction.

Uncertainty estimation for linearised inverse problems comparing Bayesian inference and a pseudoinverse approach for acoustic transmission measurements

2017 ◽  
Vol 84 (4) ◽  
Author(s):  
Nadine Feldmann ◽  
Fabian Bause ◽  
Bernd Henning
Keyword(s):  
Inverse Problem ◽  
Bayesian Inference ◽  
Statistical Approach ◽  
Uncertainty Estimation ◽  
Acoustic Transmission ◽  
Model Function ◽  
Sources Of Uncertainty ◽  
Material Parameters ◽  
Transmission Measurements

AbstractThe determination of acoustic material parameters using ultrasonic transmission measurements can mathematically be described as an inverse problem. The question concerning the influence of uncertainties on the problem's solution can be answered using a statistical approach. Therefore, the sources of uncertainty have to be identified statistically. A method for linearising the model function using the

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