Reconstructing Dispersive Scatterers With Minimal Frequency Data
01 Jan 2021-IEEE Geoscience and Remote Sensing Letters (Institute of Electrical and Electronics Engineers (IEEE))-Vol. 18, Iss: 1, pp 62-66
TL;DR: By modeling the object dispersion as a Debye medium, an inversion technique is proposed that recovers the object permittivity with a minimum number of frequencies and shows that given a properly trained neural network, single frequency reconstructions can be very competitive with multifrequency techniques that do not use neural networks.
Abstract: Reconstructing the permittivity of dispersive scatterers from the measurements of scattered electromagnetic fields is a challenging problem due to the nonlinearity of the associated optimization problem. Traditionally, this has been addressed by collecting scattered field data at multiple frequencies and using lower frequency reconstructions as a priori information for higher frequency reconstructions. By modeling the object dispersion as a Debye medium, we propose an inversion technique that recovers the object permittivity with a minimum number of frequencies. We compare the performance of this method with our recently developed deep learning based technique (Sanghvi. et al. , IEEE Trans. Comp. Imag. , 2019) and show that given a properly trained neural network, single frequency reconstructions can be very competitive with multifrequency techniques that do not use neural networks. We quantify this performance via extensive numerical examples and comment on the hardware implications of both approaches.
Citations
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TL;DR: A review of the most recent progresses in the application of ML and DL for EM vision problems is given to better understand the pros and cons and foster future research in using AI to address paramount challenges in the field of EM vision.
Abstract: In recent years, artificial intelligence (AI) techniques have been developed rapidly. With the help of big data, massive parallel computing, and optimization algorithms, machine learning (ML) and (more recently) deep learning (DL) strategies have been equipped with enhanced learning and generalization capabilities. Besides becoming an essential framework in image and speech signal processing, AI has been also widely applied to solve several electromagnetic (EM) problems with unprecedented computational efficiency, including inverse scattering and EM imaging. In this paper, a review of the most recent progresses in the application of ML and DL for such problems is given. We humbly hope a brief summary could help us to better understand the pros and cons of this research topic and foster future research in using AI to address paramount challenges in the field of EM vision.
32 citations
Journal Article•
TL;DR: A review of the most recent advances in deep learning (DL) as applied to electromagnetics (EM), antennas, and propagation is provided in this paper, aimed at giving the interested readers and practitioners in EM and related applicative fields some useful insights on the effectiveness and potentialities of deep neural networks (DNNs) as computational tools with unprecedented computational efficiency.
Abstract: A review of the most recent advances in deep learning (DL) as applied to electromagnetics (EM), antennas, and propagation is provided. It is aimed at giving the interested readers and practitioners in EM and related applicative fields some useful insights on the effectiveness and potentialities of deep neural networks (DNNs) as computational tools with unprecedented computational efficiency. The range of considered applications includes forward/inverse scattering, direction-of-arrival estimation, radar and remote sensing, and multi-input/multi-output systems. Appealing DNN-based solutions concerned with localization, human behavior monitoring, and EM compatibility are reported as well. Some final remarks are drawn along with the indications on future trends according to the authors’ viewpoint.
31 citations
TL;DR: In this paper , the authors estimate the incident field and relative permittivity of a heterogeneous dielectric object from measurements of the total electric field alone using a constrained reweighted norm minimization technique.
Abstract: Most microwave inverse imaging algorithms rely on measurements of both the total and the incident electric field in order to estimate the dielectric properties of an unknown scattering object (SO). We propose a new technique to jointly estimate the incident field and relative permittivity of a heterogeneous dielectric object from measurements of the total electric field alone. For the first task, we express the incident field as a collection of plane waves and estimate the wave coefficients from the given data by leveraging the sparsity of the plane wave spectrum and obtain the solution via a constrained reweighted $L_{1}$ norm minimization technique. Subsequently, we estimate the permittivity and geometry of the SO using a twofold subspace optimization method. We evaluate the performance of our algorithm on synthetically generated object and experimental data. For synthetic objects, the accuracy in reconstruction of the incident field and the relative permittivity is ≈93% for field measurements with a 15-dB signal-to-noise ratio, while the accuracy obtained for an experimental data set was ≈90%.
TL;DR: In this article , a multi-frequency (MF) CSI method with a multiplicative regularization (MR) is modified from the direct estimation of the contrast between dispersive scatterers and their background medium, into the alternative reconstruction of three kinds of one-pole Cole-Cole model parameters, namely, the optical relative permittivity, relative perittivity difference, and static conductivity.
Abstract: Single-pole Cole–Cole empirical models are often used for the high-precision description of the dispersion characteristics of common media, such as biological tissues, and water. The existing contrast source inversion (CSI) methods are not appropriate to reconstruct their frequency-dependent electrical properties. Therefore, one of them, a multi-frequency (MF) CSI method with a multiplicative regularization (MR), is modified from the direct estimation of the contrast between dispersive scatterers and their background medium, into the alternative reconstruction of three kinds of one-pole Cole–Cole model parameters, namely, the optical relative permittivity, relative permittivity difference, and static conductivity. Through two two-dimensional (2D) numerical experiments, the modified CSI method has been applied to detect breast tumors. The reconstructed results demonstrate preliminarily that the improved approach is feasible for the quantitative inversion of the internal breast compositions, and thus promising for breast cancer screening.
TL;DR: In this paper , a point-to-point convolutional neural network (CNN) model is proposed to reconstruct the electromagnetic parameters of multiple cavities filled with inhomogeneous anisotropic media.
Abstract: We propose a point-to-point convolutional neural network (CNN) model to reconstruct the electromagnetic parameters of multiple cavities filled with inhomogeneous anisotropic media. The input of the model is a grid matrix of electromagnetic field magnitude solved by Petrov–Galerkin finite element interface method, and the output is a distribution matrix of the electromagnetic parameters of the cavities. The uniform non-body-fitted mesh is set in the computational domain, which does not need to be updated repeatedly at the complex interfaces of different media. Compared with the standard finite element, this mesh reduction method effectively saves the cost of mesh generation. Level set functions are applied to capture these arbitrarily shaped interfaces. The matrix coefficients caused by the dielectric constant and permeability tensors of anisotropic media can also be handled with this method. The point-to-point CNN model effectively reconstructs the value and the distribution of electromagnetic parameters in the cavities, also predicting the shape and the position of the interfaces. Three optimized schemes are then proposed to improve reconstruction accuracy. Numerical results show that the size of the convolution kernel and the number of fully connected layers are the crucial parameters in determining interfaces and reducing the number of artefacts.
References
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Book•
23 May 2011TL;DR: It is argued that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas.
Abstract: Many problems of recent interest in statistics and machine learning can be posed in the framework of convex optimization. Due to the explosion in size and complexity of modern datasets, it is increasingly important to be able to solve problems with a very large number of features or training examples. As a result, both the decentralized collection or storage of these datasets as well as accompanying distributed solution methods are either necessary or at least highly desirable. In this review, we argue that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas. The method was developed in the 1970s, with roots in the 1950s, and is equivalent or closely related to many other algorithms, such as dual decomposition, the method of multipliers, Douglas–Rachford splitting, Spingarn's method of partial inverses, Dykstra's alternating projections, Bregman iterative algorithms for l1 problems, proximal methods, and others. After briefly surveying the theory and history of the algorithm, we discuss applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others. We also discuss general distributed optimization, extensions to the nonconvex setting, and efficient implementation, including some details on distributed MPI and Hadoop MapReduce implementations.
17,433 citations
"Reconstructing Dispersive Scatterer..." refers methods in this paper
...The complete algorithm is outlined as follows: 1) Procedure for MFD SOM: 1) Solve for x (1) using T-SOM at the lowest frequency 2) Estimate ws(c)p from s (c) p ∀c (Morozov’s principle) 3) Estimate wn(c)p using (2c) with x (1) at all frequencies and thereby obtain β(c)p 4) Optimize the cost function provided in (5) by iterating r and β updates using the alternating direction method of multipliers (ADMM) [20], and the conjugate gradient method, respectively (See Appendix for details of r -update)....
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...This equation is solved using the ADMM method [20]....
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...4) Optimize the cost function provided in (5) by iterating r and β updates using the alternating direction method of multipliers (ADMM) [20], and the conjugate gradient method, respectively (See Appendix for details of r -update)....
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TL;DR: The distorted Born iterative method (DBIM) is used to solve two-dimensional inverse scattering problems, thereby providing another general method to solve the two- dimensional imaging problem when the Born and the Rytov approximations break down.
Abstract: The distorted Born iterative method (DBIM) is used to solve two-dimensional inverse scattering problems, thereby providing another general method to solve the two-dimensional imaging problem when the Born and the Rytov approximations break down. Numerical simulations are performed using the DBIM and the method proposed previously by the authors (Int. J. Imaging Syst. Technol., vol.1, no.1, p.100-8, 1989) called the Born iterative method (BIM) for several cases in which the conditions for the first-order Born approximation are not satisfied. The results show that each method has its advantages; the DBIM shows faster convergence rate compared to the BIM, while the BIM is more robust to noise contamination compared to the DBIM. >
1,026 citations
"Reconstructing Dispersive Scatterer..." refers background in this paper
...It is well known that such problems, termed inverse scattering problems (ISPs), are nonlinear in nature [1], [2], and that nonlinearity plays a larger role as the object size, permittivity, or frequency increases....
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...Solutions to overcome the nonlinearity of the ISP have been extensively studied in the literature; these include iterative and algebraic schemes [1], [3]–[8], and neural network-based schemes in more recent times [9], [10] (see [11] for a review)....
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TL;DR: The theory and equations for the scattering pattern of a dielectric cylinder of arbitrary cross-section shape were developed in this paper, where the harmonic incident wave was assumed to have its electric vector parallel with the axis of the cylinder, and the field intensities were assumed to be independent of distance along the axis.
Abstract: The theory and equations are developed for the scattering pattern of a dielectric cylinder of arbitrary cross section shape. The harmonic incident wave is assumed to have its electric vector parallel with the axis of the cylinder, and the field intensities are assumed to be independent of distance along the axis. Solutions are readily obtained for inhomogeneous cylinders when the permittivity is independent of distance along the cylinder axis. Although other investigators have approximated the field within the dielectric body by the incident field, we treat the total field as an unknown function which is determined by solving a system of linear equations. In the case of the dielectric cylindrical shell of circular cross section, this technique yields results which agree accurately with the exact classical solution. Scattering patterns are also presented in graphical form for a dielectric shell of semicircular cross section, a thin homogeneous plane dielectric sheet of finite width, and an inhomogeneous plane sheet. The effects of surface-wave excitation and mutual interaction among the various portions of the dielectric shell are included automatically in this solutiom
1,000 citations
"Reconstructing Dispersive Scatterer..." refers methods in this paper
...The well-known electric field integral equation is used to formulate the ISP [18] for a 2-...
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...The well-known electric field integral equation is used to formulate the ISP [18] for a 2-D transverse magnetic [(TM), i....
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...It is well known that such problems, termed inverse scattering problems (ISPs), are nonlinear in nature [1], [2], and that nonlinearity plays a larger role as the object size, permittivity, or frequency increases....
[...]
...This presents a challenge, since the nonlinearity of the ISP gets worse as the frequency is increased....
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...Since ISPs are of interest in many imaging problems such as breast cancer detection [12], it is desirable to solve the problem at small wavelengths so as to obtain highresolution reconstructions....
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TL;DR: In this article, a simple algorithm for reconstructing the complex index of refraction of a bounded object immersed in a known background from a knowledge of how the object scatters known incident radiation is described.
Abstract: This paper describes a simple algorithm for reconstructing the complex index of refraction of a bounded object immersed in a known background from a knowledge of how the object scatters known incident radiation. The method described here is versatile accommodating both spatially and frequency varying incident fields and allowing a priori information about the scatterer to be introduced in a simple fashion. Numerical results show that this new algorithm outperforms the modified gradient approach which until now has been one of the most effective reconstruction algorithms available.
768 citations
"Reconstructing Dispersive Scatterer..." refers background in this paper
...Solutions to overcome the nonlinearity of the ISP have been extensively studied in the literature; these include iterative and algebraic schemes [1], [3]–[8], and neural network-based schemes in more recent times [9], [10] (see [11] for a review)....
[...]
TL;DR: An overview on medical imaging using microwave imaging for breast cancer and its challenges, hopes, and outlook is presented.
Abstract: Microwaves and millimeter waves have been used extensively to image dielectric bodies. The application of microwaves in biomedical imaging and diagnostics, however, remains a field with many uncharted territories. This article is an overview on medical imaging using microwave imaging for breast cancer and its challenges, hopes, and outlook.
532 citations
"Reconstructing Dispersive Scatterer..." refers background in this paper
...Since ISPs are of interest in many imaging problems such as breast cancer detection [12], it is desirable to solve...
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