Machine Learning Approach for Inverse Scattering Problem

Abstract

Recently, deep learning has significantly extended its scope from classification and low-level computer vision problems to various inverse problems such as x-ray low-dose CT, compressed sensing MRI, etc. Beyond these linear inverse problems where an off-the-shelf neural network from computer vision suffices to remove image artifacts, can machine learning learn complex non-linear physics such as photon scattering in highly diffusive medium? Here we develop a novel deep learning approach that reversely traces the photon scattering through diffusive medium to obtain an accurate 3D distribution of optical anomalies. Based on the deep convolutional framelets theory, we show that each layer of the proposed neural network actually learns the mappings that directly inverts the Lippmann-Schwinger equation and the bases of a low dimensional signal manifold. The proposed framework showed a robust performance over the various examples of the inverse problems including diffuse optical tomography (DOT) and elastic imaging. Compared to the conventional model-based approaches, the proposed deep network has many advantages. First, the inversion of the Lippmann-Swinger equation is fully data-driven such that we do not need any explicit modeling of the acquisition system and boundary conditions. Second, unlike the explicit regularization in the model-based approaches, the low-dimensional signal manifold is embedded as convolutional layers that are also learned from the data. Third, unlike the conventional approach whose performance is fixed, the proposed deep learning approach benefits from a newly gathered data by exploiting new information. Fourth, after training the network, it can reconstruct the final image within a few hundred of milliseconds since the model does not need to be re-computed per each individual data. Moreover, since the network learns a new signal representation instead of a simple denoising kernel from images to images, which is common in the convolutional neural network applications in the computer vision area, the proposed neural network is felicitous to provide a robust reconstruction in the real data even though it is only trained using a generated set of numerical data.