Combining spatial support information and shape-based method for tomographic imaging inside a microwave cylindrical scanner

Abstract

A nonlinear inverse scattering problem is solved to retrieve the permittivity maps inside a microwave cylindrical scanner of circular cross-section. In this article, we show how we can improve this minimization scheme by taking advantage of several a priori pieces of information. In particular, a global representation based on a Zernike basis expansion is introduced in order to restrain the class of solutions to functions which have circular spatial support, as is the case with the encountered geometrical configuration. The level-set function formalism is also exploited as the targets are known to be homogeneous by parts. We will show how we can combine the spatial support information and the binary nature of the scatterer, with limited changes of the inversion algorithm. Both synthetic and experimental results will be presented in order to highlight the importance of combining all the pieces of available information.

Keywords:

• level-set functions
• inverse scattering
• nonlinear optimization
• Zernike polynomial
• finite element method
• microwave imaging

AMS Subject Classifications::

• 78A46
• 78A45
• 78M10
• 78M50
• 49K20
• 90C52
• 49Q10
• 41A30
• 33C50

Acknowledgements

This work was supported in part by ANR ‘Jeunes Chercheurs’ grant JCJC06-141021 and by INTAS grant 06-1000017-8909. The authors would like to thank the referees for their constructive comments.