EISPY2D: An Open-Source Python Library for the Development and Comparison of Algorithms in Two-Dimensional Electromagnetic Inverse Scattering Problems

Microwave Imaging is an essential technique for reconstructing the electrical properties of an inaccessible medium. Many approaches have been proposed employing algorithms to solve the Electromagnetic Inverse Scattering Problem associated with this technique. In addition to the algorithm, one needs to implement adequate structures to represent the problem domain, the input data, the results of the adopted metrics, and experimentation routines. We introduce an open-source Python library that offers a modular and standardized framework for implementing and evaluating the performance of algorithms for the problem. Based on the implementation of fundamental components for the execution of algorithms, this library aims to facilitate the development and discussion of new methods. Through a modular structure organized into classes, researchers can design their case studies and benchmarking experiments relying on features such as test randomization, specific metrics, and statistical comparison. To the best of the authors’ knowledge, it is the first time that such tools for benchmarking and comparison are introduced for microwave imaging algorithms. In addition, two new metrics for location and shape recovery are presented. In this work, we introduce the principles for the design of the problem components and provide studies to exemplify the main aspects of this library. It is freely distributed through a Github repository that can be accessed from https://andre-batista.github.io/eispy2d/.

[1]  Chien-Ching Chiu,et al.  TIME DOMAIN INVERSE SCATTERING OF A TWO-DIMENSIONAL HOMOGENOUS DIELECTRIC OBJECT WITH ARBITRARY SHAPE BY PARTICLE SWARM OPTIMIZATION , 2008 .

[2]  Gaofeng Wang,et al.  A Hybrid Regularization Technique for Solving Highly Nonlinear Inverse Scattering Problems , 2018, IEEE Transactions on Microwave Theory and Techniques.

[3]  Ponnuthurai Nagaratnam Suganthan,et al.  Benchmark Functions for the CEC'2013 Special Session and Competition on Large-Scale Global Optimization , 2008 .

[4]  M. Pastorino,et al.  A Novel Microwave Imaging Approach Based on Regularization in $L^{p}$ Banach Spaces , 2012, IEEE Transactions on Antennas and Propagation.

[5]  Paolo Rocca,et al.  A REVIEW OF DEEP LEARNING APPROACHES FOR INVERSE SCATTERING PROBLEMS (INVITED REVIEW) , 2020 .

[6]  T. Isernia,et al.  Quantitative Non-Linear Inverse Scattering: A Wealth of Possibilities Through Smart Rewritings of the Basic Equations , 2021, IEEE Open Journal of Antennas and Propagation.

[7]  T. Isernia,et al.  A Simple Procedure to Design Virtual Experiments for Microwave Inverse Scattering , 2021, IEEE Transactions on Antennas and Propagation.

[8]  P. M. Berg,et al.  A contrast source inversion method , 1997 .

[9]  A. Kirsch An Introduction to the Mathematical Theory of Inverse Problems , 2021, Applied Mathematical Sciences.

[10]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.

[11]  Johan Jacob Mohr,et al.  An Introduction to Microwave Imaging for Breast Cancer Detection , 2016 .

[12]  Joel Nothman,et al.  SciPy 1.0-Fundamental Algorithms for Scientific Computing in Python , 2019, ArXiv.

[13]  M. Pastorino Qualitative Reconstruction Methods , 2010 .

[14]  MWSegEval—An image analysis toolbox for microwave breast images , 2021, SoftwareX.

[15]  R S Stein,et al.  Electromagnetic Scattering. , 1965, Science.

[16]  D. Colton,et al.  The linear sampling method in inverse electromagnetic scattering theory , 2003 .

[17]  Xudong Chen,et al.  Subspace-Based Optimization Method for Solving Inverse-Scattering Problems , 2010, IEEE Transactions on Geoscience and Remote Sensing.

[18]  Elizabeth F. Wanner,et al.  Sample size calculations for the experimental comparison of multiple algorithms on multiple problem instances , 2019, Journal of Heuristics.

[19]  W. Chew Waves and Fields in Inhomogeneous Media , 1990 .

[20]  Tommaso Isernia,et al.  Electromagnetic inverse scattering: Retrievable information and measurement strategies , 1997 .

[21]  Armand Wirgin,et al.  The inverse crime , 2004, math-ph/0401050.

[22]  Mei Song Tong,et al.  A Hybrid Quantum-Behaved Particle Swarm Optimization Algorithm for Solving Inverse Scattering Problems , 2021, IEEE Transactions on Antennas and Propagation.

[23]  Skipper Seabold,et al.  Statsmodels: Econometric and Statistical Modeling with Python , 2010, SciPy.

[24]  A. Massa,et al.  Multifrequency Particle Swarm Optimization for Enhanced Multiresolution GPR Microwave Imaging , 2017, IEEE Transactions on Geoscience and Remote Sensing.

[25]  Weng Cho Chew,et al.  An iterative solution of the two‐dimensional electromagnetic inverse scattering problem , 1989, Int. J. Imaging Syst. Technol..

[26]  J. Richmond Scattering by a dielectric cylinder of arbitrary cross section shape , 1965 .

[27]  R. Kress,et al.  Inverse Acoustic and Electromagnetic Scattering Theory , 1992 .

[28]  Xudong Chen,et al.  Computational Methods for Electromagnetic Inverse Scattering , 2018 .

[29]  Kalyanmoy Deb,et al.  Self-Adaptive Genetic Algorithms with Simulated Binary Crossover , 2001, Evolutionary Computation.

[30]  Mahta Moghaddam,et al.  A Fast Level Set Method for Multimaterial Recovery in Microwave Imaging , 2018, IEEE Transactions on Antennas and Propagation.

[31]  A. E. Eiben,et al.  Introduction to Evolutionary Computing , 2003, Natural Computing Series.

[32]  C. Chiu,et al.  Image reconstruction of a perfectly conducting cylinder by the genetic algorithm , 1996 .

[33]  Lucas S. Batista,et al.  A Quadratic Programming Approach for Microwave Imaging , 2021, IEEE Transactions on Antennas and Propagation.

[34]  Marek E. Bialkowski,et al.  Microwave head imaging for stroke detection , 2011 .

[35]  C. Fletcher Computational Galerkin Methods , 1983 .

[36]  Hussein Attia,et al.  Review of Microwaves Techniques for Breast Cancer Detection , 2020, Sensors.

[37]  W. Chew,et al.  Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method. , 1990, IEEE transactions on medical imaging.

[38]  Joe LoVetri,et al.  Evaluating Performance of Microwave Image Reconstruction Algorithms: Extracting Tissue Types with Segmentation Using Machine Learning , 2021, J. Imaging.

[39]  Weng Cho Chew,et al.  Comparison of the born iterative method and tarantola's method for an electromagnetic time‐domain inverse problem , 1991, Int. J. Imaging Syst. Technol..

[40]  A. Massa,et al.  A Differential Evolution-based iterative multi-scaling algorithm for microwave imaging of dielectric structures , 2010, 2010 IEEE International Conference on Imaging Systems and Techniques.

[41]  J. LoVetri,et al.  Comparison of an Enhanced Distorted Born Iterative Method and the Multiplicative-Regularized Contrast Source Inversion method , 2009, IEEE Transactions on Antennas and Propagation.

[42]  Matteo Pastorino,et al.  Quantitative Microwave Imaging Method in Lebesgue Spaces With Nonconstant Exponents , 2018, IEEE Transactions on Antennas and Propagation.

[43]  Anyong Qing Dynamic differential evolution strategy and applications in electromagnetic inverse scattering problems , 2006, IEEE Transactions on Geoscience and Remote Sensing.

[44]  Chiang Ching Shan Microwave Imaging , 1979, 1979 9th European Microwave Conference.

[45]  P. Rocca,et al.  Evolutionary optimization as applied to inverse scattering problems , 2009 .

[46]  Warren Hare,et al.  Best practices for comparing optimization algorithms , 2017, Optimization and Engineering.

[47]  Edward J. Baranoski,et al.  Through wall imaging: Historical perspective and future directions , 2008, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing.

[48]  P. Rocca,et al.  Differential Evolution as Applied to Electromagnetics , 2011, IEEE Antennas and Propagation Magazine.

[49]  Matteo Pastorino Microwave Imaging Strategies, Emerging Techniques, and Future Trends , 2010 .

[50]  Ching-Chuan Su,et al.  Calculation of electromagnetic scattering from a dielectric cylinder using the conjugate gradient method and FFT , 1987 .