Subwavelength micro-structure probing by binary-specialized methods: contrast source and convolutional neural networks
Résumé
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.
Sub-wavelength distances between adjacent rods and subwavelength
rod diameters are assumed and it leads to a severe
challenge due to need of super-resolution within the present
micro-structure, far beyond the Rayleigh criterion. A binary case
is focused onto herein: all rods have same permittivity, but an
unknown number of them is missing, the aim being to detect
those within the resulting damaged micro-structure from far-field
data. Two binary-specialized methods are developed to that effect
and discussed in depth. 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
it uses convolutional neural networks (CNN). The CSI version
is mostly used as reference for the CNN one. Comprehensive
numerical simulations in configurations of interest in terms of
organization of the micro-structure, 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.