Two-dimensional inverse scattering solution using NURBS expansion and a deep learning method

This paper presents a novel framework for solving two-dimensional (2D) inverse scattering problems by integrating nonuniform rational B-spline (NURBS) parameterization with convolutional neural networks (CNNs). Tra ditional pixel/voxel-based deep learning methods often suffer from high dimensionality and discretization artifacts, while purely geometric approaches lack robust inversion mechanisms. To address these limitations, we propose a hybrid frame work where the relative permittivity profile of an unknown scatterer is compactly represented as a NURBS surface, parameterized by a sparse set of control points and weights. This approach reduces the problem dimensionality over 16 times. On the other hand, using NURBS expansion ensures material continuity. The scattered electric and magnetic f ields are simulated using the 2D finite-difference time-domain (FDTD) method, and a CNN is trained to map time domain scattered field measurements probed around the device under test, directly to the NURBS control points. The results demonstrate that the framework achieves accurate reconstructions, with a root mean squared error of 0.012, while maintaining computational efficiency and robustness to noise.