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Efficient and accurate inversion of multiple scattering with deep learning

This is the python implementation of the deep leraning model ScaDec for inverting multiple light scattering in a surpervised manner. The paper is originally published on Optics Express. The arxiv version of the paper is available here

Abstract

Image reconstruction under multiple light scattering is crucial in a number of applications such as diffraction tomography. The reconstruction problem is often formulated as a nonconvex optimization, where a nonlinear measurement model is used to account for multiple scattering and regularization is used to enforce prior constraints on the object. In this paper, we propose a powerful alternative to this optimization-based view of image reconstruction by designing and training a deep convolutional neural network that can invert multiple scattered measurements to produce a high-quality image of the refractive index. Our results on both simulated and experimental datasets show that the proposed approach is substantially faster and achieves higher imaging quality compared to the state-of-the-art methods based on optimization.

Experimental Results

The following two figures show the visual results of ScaDec on simulated and experimental datasets (CelebA & Fresnel). The ScaDec substantially outperforms the optimization-based methods.

visualExamples

expExamples

Trianing & Testing

The scripts train.py and test.py are for training and testing the model ScaDec. If you want to train your own ScaDec, please checkout these two files. We also share pre-trained model and code here. Please cite the paper if you find our work useful for your research. The matlab code does

(1) generating measurements by solving 2D Lippmann Schwinger Equation

(2) generating syntheized Gaussian piece-wise smoothed elipses

(3) generating syntheized circles for Fresnel 2D

(4) backpropagation

To train/test a ScaDec, simply type:

  python train.py
  python test.py

Environment Requirement

Tensorflow v1.4
PIL
Python 3.6
Scipy

Citation

If you find the paper useful in your research, please cite the paper:

  @article{{Sun:18,
  Author = {Yu Sun and Zhihao Xia and Ulugbek S. Kamilov},
  Doi = {10.1364/OE.26.014678},
  Journal = {Opt. Express},
  Keywords = {Image reconstruction techniques; Inverse problems; Tomographic image processing; Inverse scattering},
  Month = {May},
  Number = {11},
  Pages = {14678--14688},
  Publisher = {OSA},
  Title = {Efficient and accurate inversion of multiple scattering with deep learning},
  Url = {http://www.opticsexpress.org/abstract.cfm?URI=oe-26-11-14678},
  Volume = {26},
  Year = {2018},
  Bdsk-Url-1 = {http://www.opticsexpress.org/abstract.cfm?URI=oe-26-11-14678},
  Bdsk-Url-2 = {https://doi.org/10.1364/OE.26.014678}}

Erratum

In the paper, the feature dimension of ScaDec is mistyped in Fig.3. The corrected feature figure is shown here.

ScaDecArch

Thanks Jiaming for pointing out this typo. If you have any concerns about this paper, feel free to contact us: sun.yu@wustl.edu