scholarly journals A Multiplicative Regularizer Augmented with Spatial Priors for Microwave Imaging

2020 ◽  
Author(s):  
Nozhan Bayat ◽  
Puyan Mojabi
Keyword(s):  
Experimental Data ◽  
Total Variation ◽  
Prior Information ◽  
Microwave Imaging ◽  
Minimal Change ◽  
Data Sets ◽  
Quantitative Accuracy ◽  
L2 Norm ◽  
Imaging Algorithms ◽  
Multiplicative Regularization

The standard weighted L2 norm total variation multiplicative regularization (MR) term originally developed for microwave imaging algorithms is modified to take into account<br>structural prior information, also known as spatial priors (SP), about the object being imaged. This modification adds one extra term to the integrand of the standard MR, thus, being referred to as an augmented MR (AMR). The main advantage of the proposed approach is that it requires a minimal change to the existing microwave imaging algorithms that are already equipped with the MR. Using two experimental data sets, it is shown that the proposed AMR (i) can handle partial SP, and (ii) can, to some extent, enhance the quantitative accuracy achievable from<br>microwave imaging.

scholarly journals A Multiplicative Regularizer Augmented with Spatial Priors for Microwave Imaging

2020 ◽  
Author(s):  
Nozhan Bayat ◽  
Puyan Mojabi
Keyword(s):  
Experimental Data ◽  
Total Variation ◽  
Prior Information ◽  
Microwave Imaging ◽  
Minimal Change ◽  
Data Sets ◽  
Quantitative Accuracy ◽  
L2 Norm ◽  
Imaging Algorithms ◽  
Multiplicative Regularization

The standard weighted L2 norm total variation multiplicative regularization (MR) term originally developed for microwave imaging algorithms is modified to take into account<br>structural prior information, also known as spatial priors (SP), about the object being imaged. This modification adds one extra term to the integrand of the standard MR, thus, being referred to as an augmented MR (AMR). The main advantage of the proposed approach is that it requires a minimal change to the existing microwave imaging algorithms that are already equipped with the MR. Using two experimental data sets, it is shown that the proposed AMR (i) can handle partial SP, and (ii) can, to some extent, enhance the quantitative accuracy achievable from<br>microwave imaging.

scholarly journals A Multiplicative Regularizer Augmented with Spatial Priors for Microwave Imaging

2020 ◽  
Author(s):  
Nozhan Bayat ◽  
Puyan Mojabi
Keyword(s):  
Experimental Data ◽  
Total Variation ◽  
Prior Information ◽  
Microwave Imaging ◽  
Minimal Change ◽  
Data Sets ◽  
Quantitative Accuracy ◽  
L2 Norm ◽  
Imaging Algorithms ◽  
Multiplicative Regularization

The standard weighted L2 norm total variation multiplicative regularization (MR) term originally developed for microwave imaging algorithms is modified to take into account<br>structural prior information, also known as spatial priors (SP), about the object being imaged. This modification adds one extra term to the integrand of the standard MR, thus, being referred to as an augmented MR (AMR). The main advantage of the proposed approach is that it requires a minimal change to the existing microwave imaging algorithms that are already equipped with the MR. Using two experimental data sets, it is shown that the proposed AMR (i) can handle partial SP, and (ii) can, to some extent, enhance the quantitative accuracy achievable from<br>microwave imaging.

scholarly journals Phaseless Gauss-Newton Inversion for Microwave Imaging

2020 ◽  
Author(s):  
Chaitanya Narendra ◽  
Puyan Mojabi
Keyword(s):  
Field Data ◽  
Prior Information ◽  
Structural Information ◽  
Microwave Imaging ◽  
The Other ◽  
Total Field ◽  
Field Phase ◽  
Full Data ◽  
L2 Norm ◽  
Phase Data

<p>A phaseless Gauss-Newton inversion (GNI) algorithm is developed for microwave imaging applications. In contrast to full-data microwave imaging inversion that uses complex (magnitude and phase) scattered field data, the proposed phaseless GNI algorithm inverts phaseless (magnitude-only) total field data. This phaseless Gauss-Newton inversion (PGNI) algorithm is augmented with three different forms of regularization, originally developed for complex GNI. First, we use the standard weighted L2 norm total variation multiplicative regularizer which is appropriate when there is no prior information about the object being imaged. We then use two other forms of regularization operators to incorporate prior information about the object being imaged into the PGNI algorithm. The first one, herein referred to as SL-PGNI, incorporates prior information about the expected relative complex permittivity values of the object of interest. The other, referred to as SP-PGNI, incorporates spatial priors (structural information) about the objects being imaged. The use of prior information aims to compensate for the lack of total field phase data. The PGNI, SL-PGNI, and SP-PGNI inversion algorithms are then tested against synthetic and experimental phaseless total field data.</p>

scholarly journals Phaseless Gauss-Newton Inversion for Microwave Imaging

2020 ◽  
Author(s):  
Chaitanya Narendra ◽  
Puyan Mojabi
Keyword(s):  
Field Data ◽  
Prior Information ◽  
Structural Information ◽  
Microwave Imaging ◽  
The Other ◽  
Total Field ◽  
Field Phase ◽  
Full Data ◽  
L2 Norm ◽  
Phase Data

<p>A phaseless Gauss-Newton inversion (GNI) algorithm is developed for microwave imaging applications. In contrast to full-data microwave imaging inversion that uses complex (magnitude and phase) scattered field data, the proposed phaseless GNI algorithm inverts phaseless (magnitude-only) total field data. This phaseless Gauss-Newton inversion (PGNI) algorithm is augmented with three different forms of regularization, originally developed for complex GNI. First, we use the standard weighted L2 norm total variation multiplicative regularizer which is appropriate when there is no prior information about the object being imaged. We then use two other forms of regularization operators to incorporate prior information about the object being imaged into the PGNI algorithm. The first one, herein referred to as SL-PGNI, incorporates prior information about the expected relative complex permittivity values of the object of interest. The other, referred to as SP-PGNI, incorporates spatial priors (structural information) about the objects being imaged. The use of prior information aims to compensate for the lack of total field phase data. The PGNI, SL-PGNI, and SP-PGNI inversion algorithms are then tested against synthetic and experimental phaseless total field data.</p>

scholarly journals On the Numerical Implementation of the Multiplicative Regularization in Microwave Imaging

2020 ◽  
Author(s):  
Puyan Mojabi
Keyword(s):  
High Spatial Frequency ◽  
Positive Definite ◽  
Microwave Imaging ◽  
Numerical Implementation ◽  
Discrete Operator ◽  
Source Inversion ◽  
Contrast Source Inversion ◽  
L2 Norm ◽  
Frequency Components ◽  
Multiplicative Regularization

<p> We consider the widely-used weighted L2 norm total variation multiplicative regularizer (MR) for both the Gauss-Newton inversion (GNI) and contrast source inversion (CSI) algorithms in microwave imaging (MWI). It is shown that the proper numerical implementation of the discretized MR operator is important for the GNI algorithm whereas the CSI algorithm is more robust with respect to different implementations of this MR. For the GNI algorithm, the MR operator should be discretized such that high spatial frequency components are not present in its nullspace, and also the resulting discrete operator is positive definite.</p>

scholarly journals On the Numerical Implementation of the Multiplicative Regularization in Microwave Imaging

2020 ◽  
Author(s):  
Puyan Mojabi
Keyword(s):  
High Spatial Frequency ◽  
Positive Definite ◽  
Microwave Imaging ◽  
Numerical Implementation ◽  
Discrete Operator ◽  
Source Inversion ◽  
Contrast Source Inversion ◽  
L2 Norm ◽  
Frequency Components ◽  
Multiplicative Regularization

<p> We consider the widely-used weighted L2 norm total variation multiplicative regularizer (MR) for both the Gauss-Newton inversion (GNI) and contrast source inversion (CSI) algorithms in microwave imaging (MWI). It is shown that the proper numerical implementation of the discretized MR operator is important for the GNI algorithm whereas the CSI algorithm is more robust with respect to different implementations of this MR. For the GNI algorithm, the MR operator should be discretized such that high spatial frequency components are not present in its nullspace, and also the resulting discrete operator is positive definite.</p>

scholarly journals Polyconvex hyperelastic modeling of rubberlike materials

2021 ◽  
Vol 43 (7) ◽  
Author(s):  
Cyprian Suchocki ◽  
Stanisław Jemioło
Keyword(s):  
Experimental Data ◽  
Power Law ◽  
Curve Fitting ◽  
Constitutive Relations ◽  
Data Sets ◽  
Power Law Model ◽  
Stored Energy ◽  
Data Approximation ◽  
Exponential Power ◽  
Hyperelastic Models

AbstractIn this work a number of selected, isotropic, invariant-based hyperelastic models are analyzed. The considered constitutive relations of hyperelasticity include the model by Gent (G) and its extension, the so-called generalized Gent model (GG), the exponential-power law model (Exp-PL) and the power law model (PL). The material parameters of the models under study have been identified for eight different experimental data sets. As it has been demonstrated, the much celebrated Gent’s model does not always allow to obtain an acceptable quality of the experimental data approximation. Furthermore, it is observed that the best curve fitting quality is usually achieved when the experimentally derived conditions that were proposed by Rivlin and Saunders are fulfilled. However, it is shown that the conditions by Rivlin and Saunders are in a contradiction with the mathematical requirements of stored energy polyconvexity. A polyconvex stored energy function is assumed in order to ensure the existence of solutions to a properly defined boundary value problem and to avoid non-physical material response. It is found that in the case of the analyzed hyperelastic models the application of polyconvexity conditions leads to only a slight decrease in the curve fitting quality. When the energy polyconvexity is assumed, the best experimental data approximation is usually obtained for the PL model. Among the non-polyconvex hyperelastic models, the best curve fitting results are most frequently achieved for the GG model. However, it is shown that both the G and the GG models are problematic due to the presence of the locking effect.

scholarly journals BioNetLink - An Architecture for Working with Network Data

2014 ◽  
Vol 11 (2) ◽  
pp. 68-79
Author(s):  
Matthias Klapperstück ◽  
Falk Schreiber
Keyword(s):  
Experimental Data ◽  
Biological Networks ◽  
Regulatory Networks ◽  
Large Data ◽  
Biological Data ◽  
Network Data ◽  
Data Sets ◽  
Dynamic Views ◽  
Gene Regulatory ◽  
Multiple Network

Summary The visualization of biological data gained increasing importance in the last years. There is a large number of methods and software tools available that visualize biological data including the combination of measured experimental data and biological networks. With growing size of networks their handling and exploration becomes a challenging task for the user. In addition, scientists also have an interest in not just investigating a single kind of network, but on the combination of different types of networks, such as metabolic, gene regulatory and protein interaction networks. Therefore, fast access, abstract and dynamic views, and intuitive exploratory methods should be provided to search and extract information from the networks. This paper will introduce a conceptual framework for handling and combining multiple network sources that enables abstract viewing and exploration of large data sets including additional experimental data. It will introduce a three-tier structure that links network data to multiple network views, discuss a proof of concept implementation, and shows a specific visualization method for combining metabolic and gene regulatory networks in an example.

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