Quantitative Diffraction Tomography for Weak Scatterers Based on Aliasing Modification of the Multifrequency Spatial Spectrum

Diffraction tomography (DT) is a linear approach to solving electromagnetic inverse scattering problems. Based on the weak scattering assumptions (such as Born or Rytov approximations), the spatial spectrum of the contrast at one certain frequency is a linear mapping of the scattered field data. As is well-known, using more frequencies means better performance of noise suppression. However, the spatial spectra are aliased in cases of multifrequency data. In addition, the permittivity and the conductivity are coupled in the aliased multifrequency spatial spectrum. In this article, a quantitative DT for weak scatterers is proposed by first doing a coordinate transformation, then decoupling the permittivity and the conductivity, and finally modifying the aliased multifrequency spatial spectrum. In doing so, the modified spatial spectra of the permittivity and conductivity are formulated, respectively, leading to a quantitative DT for weak scatterers based on aliasing modification of the multifrequency spectrum. Inversion results with synthetic and experimental data demonstrate that the proposed method outperforms the conventional DT approach in terms of quantitative inversion accuracy for weak scatterers of multifrequency data while maintaining the anti-noise performance.