Equidistant Sub-Nyquist 3-D Microwave Imaging Using Rational Thin-Plate Spline Interpolation

High sampling rates required by the Nyquist sampling theorem impose limitations on both rapid data acquisition and measurement system design in planar microwave holographic imaging, rendering sub-Nyquist sampling a desirable feature. Compared to the incoherence requirement in compressed-sensing-based methods, equidistant sampling schemes are favorable for a more general and intuitive system design. In this paper, a 3D microwave imaging scheme using equidistant sub-Nyquist samples is proposed. The method is based on the open-circuit voltage formulation in [1], but the reconstruction with sub-Nyquist data is done using the rational thin-plate spline (RTPS) interpolation. Determination of the interpolation function involves finding an eigenvector with the smallest eigenvalue to a generalized eigenproblem. A remedy procedure is also developed to address the singularities or outliers produced by the ill-conditioning in such a problem. The effectiveness and robustness of the developed method are verified with numerical experiments in X-band, showing significant improvements in image quality.