A Deep Learning Framework for Three Dimensional Shape Reconstruction from Phaseless Acoustic Scattering Far-field Data

TL;DR

This work tackles the problem of reconstructing 3D scatterer shapes from phaseless acoustic far-field data using a single incident wave at a single frequency. The authors propose ISSRNet, a data-driven framework that builds a smooth latent shape space with a 3D variational auto-encoder and learns a mapping from phaseless scattering data to this latent space via an inverse network, optionally augmented by a forward network for regularization. The approach is evaluated on synthetic random particles and ShapeNet airplanes/cars, achieving accurate global and local shape reconstructions with a dramatic speed-up over traditional forward solves (e.g., predicting hundreds of shapes in seconds vs. solver times of hundreds of seconds per object). Key findings include that a purely shape-space loss suffices for good reconstructions on complex 3D shapes, and that the framework does not rely on forward solves during inference. Overall, ISSRNet offers a fast, data-driven solution to a historically ill-posed problem with practical implications for sonar, NDT, and medical imaging.

Abstract

The inverse scattering problem is of critical importance in a number of fields, including medical imaging, sonar, sensing, non-destructive evaluation, and several others. The problem of interest can vary from detecting the shape to the constitutive properties of the obstacle. The challenge in both is that this problem is ill-posed, more so when there is limited information. That said, significant effort has been expended over the years in developing solutions to this problem. Here, we use a different approach, one that is founded on data. Specifically, we develop a deep learning framework for shape reconstruction using limited information with single incident wave, single frequency, and phase-less far-field data. This is done by (a) using a compact probabilistic shape latent space, learned by a 3D variational auto-encoder, and (b) a convolutional neural network trained to map the acoustic scattering information to this shape representation. The proposed framework is evaluated on a synthetic 3D particle dataset, as well as ShapeNet, a popular 3D shape recognition dataset. As demonstrated via a number of results, the proposed method is able to produce accurate reconstructions for large batches of complex scatterer shapes (such as airplanes and automobiles), despite the significant variation present within the data.

Figures (14)

• Figure 1: Data pre-processing step for ShapeNet meshes. The left column contains the original meshes that are not watertight and have poor-quality triangulation. The meshes in the right column show the remeshing product.
• Figure 2: Random particles from the data set
• Figure 3: Proposed deep learning pipeline. The color-coded pre-trained generator and inverse encoder modules can be found in Figures \ref{['fig:Figure4']} and \ref{['fig:Figure5']}, respectively. The pipeline can be trained using two different loss functions, $Loss_{Shape}$ which is the Chamfer distance between the generated and target point-clouds; $Loss_{FarField}$ which is the mean-squared error between the output and input scattered fields.
• Figure 4: (color online) 3D Auto-encoder Architecture
• Figure 5: Inverse network architecture. A convolutional neural network is used to perform feature extraction from the input scattered field. The resulting shape feature vector is then processed with the variational sampler to sample from $q(z|x)$, which can be decoded using the pre-trained auto-encoder generator.