A Topological Regularization Term for Inverse Scattering Problems

Inverse scattering algorithms seek to reconstruct the support and wave properties of an object through knowledge of transmitted signals and measured scattered waves. There are a myriad of techniques for reconstructing a scatterer that provide unique advantages in different imaging environments. It would thus be beneficial to use knowledge from an inverse scattering reconstruction obtained using one algorithm to improve imaging performance using a different technique. We propose incorporating prior information concerning the topology of the object being imaged into a regularization term constructed using persistent homology. The topological regularization term penalizes reconstructions which have an incorrect number of connected components and loops and updates the image to better match previous information. We aim to improve the quality of quantitative reconstructions obtained using the well-known distorted Born iterative method (DBIM) through the use of this topological regularization term. Reconstructions from simulated data and a variety of scatterers show that the addition of this novel regularization term can improve the fidelity of images obtained using DBIM and preserve topological features of the object being imaged.