X-ray phase contrast imaging permits to reach nanometric resolution in tomographic imaging with several orders of magnitude higher sensitivity than using the attenuation [1]. The main drawback is that it needs an additional reconstruction step, known as phase retrieval, to yield quantitative images. This reconstruction problem is a non-linear inverse problem. We have previously developed algorithms based on linear approximations, as well as non-linear approaches, to solve this problem. The non-linear problem remains difficult to treat, however. In contrast, the direct problem of generating phase contrast images is relatively straight forward. This makes phase retrieval in X-ray phase contrast imaging a prime candidate for machine learning based inversion approaches.

The goal of this internship is to use deep learning for phase retrieval from X-ray phase contrast images. In particular, we will investigate various deep learning architectures and deep learning inversion approaches [2] and compare them to model-based approaches.

The main challenge is to find an appropriate network structure for the problem. Therefore, several networks from literature will be applied in the problem.

A challenge will be the management of free physical parameters in the problem, such as X-ray energy, propagation distance, and imaging resolution.

Imaging parameters will have to be optimised for this class of reconstruction algorithms. This includes the possibility of using one or several propagation distances, the distances used, and the contrast in the images.

The training of networks will have to be addressed. Some types of algorithms, for example for post processing of imaging artifacts, might be possible to train directly on the acquired data. Other approaches probably should be trained on simulated data and on images of phantoms of known composition. The accurate simulation of phase contrast data will be investigated in another PhD subject.

The expected contributions are:

- Evaluation of deep learning approaches in literature on the X-ray phase contrast problem, and comparison to model based approaches
- Propositions for taking into account the different physical parameters such as propagation distance, energy and resolution
- Proposition of new deep learning based algorithms, for example combining iterative reconstruction schemes and machine learning algorithms

The first approach considered will be to optimize a reconstruction network trained to map the measured data and the reconstructed image [3, 4]. Recently, several iterative approaches have been proposed using deep learning method to improve the results obtained with classical iterative approaches for inverse problems [5]. They will be adapted to the inverse problem set by the phase retrieval problem. We will also investigate the new methods to solve inverse problems based on Generative Adversarial Networks [6-7].

Training data sets will be generated using in-house software. Deep learning methods will be implemented using TensorFlow, PyTorch and specialised libraries in Python. The developed methods will be compared to previously developed algorithms on data from the European Synchrotron Radiation Facility (ESRF), Grenoble, France, and MAX IV, Lund, Sweden. Developed algorithms will be included in the PyPhase phase retrieval software.

The profile of the candidate:

Engineering or MSc degree in physics, mathematics, computer science or related discipines.

Experience in image processing and programming in Python and required.

Experience in deep learning for image processing, programming in Matlab and C++, and mathematics relevant to the problem strongly appreciated.

[1] R. Mokso, P. Cloetens, E. Maire, W. Ludwig, and J.-Y. BuffieÌre, “Nanoscale zoom tomography with hard x rays using Kirkpatrick-Baez optics,” Appl. Phys. Lett. 90, 144104, 2007.

[2] Y. LeCun, Y. Bengio, and G. Hinton, “Deep learning,” Nature 521, 436, 2015.

[3] K. H. Jin, M. T. McCann, E. Froustey, and M. Unser. Deep convolutional neural network for inverse problems in imaging IEEE Tran. Image Process 26(9) : 4509-4522 , 2017

[4] A.Adler, O.Oktem Solving inverse ill-posed problems using iterative deep neural networks Inverse Problems 33(12), 124007, 2017.

[5] A.Hauptman, F.Lucka, M.Betcke, J.Adler, B.Cox, P.Beard, S.Ourselin, S.Arridge Model based learning for accelerated, limited-view 3D photoacoustic tomography IEEE Transactions on medical imaging 37(6) 1382-1393, 2018.

[6] J.T.Guibas, T.S.Virdi and P.S.Li “Synthetic medical images from dual generative adversarial networks”, https://arxiv.org/abs/1708.01872

[7] J.Adler and S.Lunz Banach Wasserstein GAN, Advances in Neural Information Processing Systems (NIPS 2018), Curran Associates, pp.6754-6763.