Subwavelength Microstructure Probing by Binary- Specialized Methods: Contrast Source and Convolutional Neural Networks

Time-harmonic transverse-magnetic electromagnetic probing of a grid-like, finite set of infinitely long circular cylindrical dielectric rods affected by missing ones is investigated. Subwavelength distances between adjacent rods and subwavelength rod diameters are assumed, and this leads to a severe challenge due to the need of superresolution within the present microstructure, well beyond the Rayleigh criterion. A binary case is focused on: all rods have the same permittivity, but an unknown number of them are missing, the aim being to detect those within the resulting damaged microstructure from far-field data. Two binary-specialized methods are developed to that effect. One builds upon the iterative contrast-source inversion (CSI) with enforcing a binary contrast inside it. The other is set within a machine learning framework and uses convolutional neural networks (CNNs). The CSI version is mostly used as a reference for the CNN one. Comprehensive numerical simulations in configurations of interest in terms of organization of the microstructure, missing rods, frequency of observation, data acquisition, and noise are proposed. The binary-specialized CNN method appears powerful, upon proper training as expected, and outperforms the binary-specialized CSI method in terms of computational burden, quality of the probing, and versatility.