Reconstruction of inhomogeneous media by an iteration algorithm with a learned projector

TL;DR

This paper introduces a deep learning-enhanced iterative algorithm combining a learned projector with traditional methods to improve the reconstruction of inhomogeneous media from acoustic data, addressing ill-posedness and nonlinearity.

Contribution

It proposes a novel deep learning-based iterative reconstruction method that integrates a learned projector to incorporate a priori shape information, enhancing accuracy and robustness.

Findings

Effective reconstruction even for high contrast media

Good generalization ability demonstrated in experiments

Outperforms traditional methods in accuracy

Abstract

This paper is concerned with the inverse problem of reconstructing an inhomogeneous medium from the acoustic far-field data at a fixed frequency in two dimensions. This inverse problem is severely ill-posed (and also strongly nonlinear), and certain regularization strategy is thus needed. However, it is difficult to select an appropriate regularization strategy which should enforce some a priori information of the unknown scatterer. To address this issue, we plan to use a deep learning approach to learn some a priori information of the unknown scatterer from certain ground truth data, which is then combined with a traditional iteration method to solve the inverse problem. Specifically, we propose a deep learning-based iterative reconstruction algorithm for the inverse problem, based on a repeated application of a deep neural network and the iteratively regularized Gauss-Newton method (IRGNM). Our deep neural network (called the learned projector in this paper) mainly focuses on learning the a priori information of the shape of the unknown contrast with a normalization technique in the training process and is trained to act like a projector which is helpful for projecting the solution into some feasible region. Extensive numerical experiments show that our reconstruction algorithm provides good reconstruction results even for the high contrast case and has a satisfactory generalization ability.