Reconstruction of inhomogeneous media by iterative reconstruction algorithm with learned projector

Abstract

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves from an inhomogeneous medium in two dimensions. We propose a deep learningbased iterative reconstruction algorithm for recovering the contrast of the inhomogeneous medium from the far-field data. The proposed algorithm is given by repeated applications of the Landweber method, the iteratively regularized Gauss-Newton method (IRGNM) and a deep neural network. The Landweber method is used to generate initial guesses for the exact contrast, and the IRGNM is employed to make further improvements to the estimated contrast. 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 by using a normalization technique in the training process and is trained to act like a projector which is expected to make the estimated contrast obtained by the Landweber method or the IRGNM closer to the exact contrast. It is believed that the application of the normalization technique can release the burden of training the deep neural network and lead to good performance of the proposed algorithm. Furthermore, the learned projector is expected to provide good initial guesses for IRGNM and be helpful for accelerating the proposed algorithm. Extensive numerical experiments show that our inversion algorithm has a satisfactory reconstruction capacity and good generalization ability.

A direct sampling-based deep learning approach for inverse medium scattering problems

“…In this numerical experiment, there are 16 receivers located on Γ and the sources of the incident fields are still equally distributed on the circle, and we employ the functions (38) as the inputs of the neural networks for both training and testing. The data augmentations are not used in this example as the rotation and symmetry properties of the index functions do not hold for this case.…”

“…A Two-step enhanced deep learning approach invented in [54] consists of an initial guess step and a refinement step by introducing two convolutional neural networks. An iterative reconstruction algorithm called Learned Combined Algorithm was proposed in [38] to reconstruct the inhomogeneous media from the far-field data by repeatedly applying the Landweber approach, the iteratively regularized Gauss-Newton method, and the deep neural projector. In [21], by employing a few parameters to represent the star-shaped scatterers, the authors designed a fully connected neural network for recovering the scatterer from measured scattered data with only a single incident field.…”