Inverse problems in X-ray phase retrieval and tomography

Thursday 4 Apr 2019, 08:30 → 19:35 Europe/Stockholm

Workshop room, 5th floor (LINXS)

Scope:

Create an overview of activities in the region related to phase retrieval and tomographic reconstruction. Enable collaboration and highlight possible new projects and discuss the possibility of their realisation / funding. The participants (15-30) will be mathematicians, physicists and computing scientists. Existing tools (software packages) will be demonstrated in a form of short hands-on sessions. 

Keynotes:

Doga Gursoy, Northwestern University, USA 

Per Christian Hansen, Section for Scientific Computing, DTU Compute

Daniel Pelt, CWI Amsterdam

Jonas Adler, KTH Stockholm 

Max Langer, Creatis, INSA Lyon

Viktor Nikitin, MAX IV and Advanced Photon Source

Marcus Carlsson, Lund University

 

Format:  1 day 

Sessions: 
morning:    1. inverse problems: (i) phasing and (ii) tomo reconstruction ;
                    2. implementation of existing algorithms;
afternoon: 3. hands-on with existing tools and discussion corners

08:30 → 09:00 registration with breakfast

09:00 → 10:40 invited talks: Phase retrieval

09:10 Doga Gursoy, Northwestern University & Argonne National Lab.

Ptycho-tomography: An emerging lensless microscopy technique for imaging materials at the nanoscale

The increasing availability of coherent light sources at short wavelengths from the extreme ultraviolet to the hard x-ray regime has paved the way for widespread use of coherent diffraction imaging (CDI) techniques in the past decade. In contrast to classical microscopy, CDI does not require an objective lens between the sample and the detector, therefore it can provide spatial resolution with no lens-imposed limitations. In contrast to classical CDI, imaging of wide field-of-views can be achieved by performing CDI in scanning mode. This approach is commonly known as “ptychography” following the work of Hegerl and Hoppe on electron microscopy in 1969. However while ptychography with current and future synchrotron-based X-ray sources is very versatile, the main advantage of its diffraction-limited spatial resolution is diminished by the inherently limited temporal resolution in obtaining 3D images. In this talk I will talk on a set of new computational methods that can yield superior reconstructions for high-speed or photon-limited imaging conditions when implemented as an integral part of the imaging setup.

09:40 Max Langer, Creatis, INSA Lyon, France

Some methodological contributions to X-ray phase contrast imaging

I present some of our methodological contributions to X-ray phase contrast imaging. Phase retrieval often suffers from noise in the low spatial frequencies. We proposed a prior on the imaged object based on an attenuation image to regularise the low spatial frequencies in the retrieved phase. For the experimental setup, we showed that spreading the imaging dose over several propagation distances can improve reconstructed image quality for a given imaging dose. When using multiple propagation distances, we showed that the choice of registration algorithm can have an effect on the reconstructed image quality. Finally, I will give a first preview of a phase retrieval code under development, which aim is to facilitate development and reimplementation of phase retrieval algorithms and the handling of data from different sources.

10:10 Marcus Carlsson, Lund University

PhaseLift, possibilities and challenges.

The phase retrieval problem is ill posed, and most phase retrieval algorithms stabilize inversion via additional assumptions on the support of the object. These algorithms come without guarantee of convergence, and it is a problem in practice. PhaseLift is a new (2013) algorithm which is based on a completely different approach, and it stabilizes the inversion by the use of e.g. masks. I will describe this algorithm, describe drawbacks (slow) possible improvements (work in progress with D. Gerosa) and ultimately ask the audience; is this a potential candidate for processing of synchrotron data?

10:40 → 11:00 coffee

11:00 → 12:10 invited talks: tomographic reconstruction

11:00 Per Christian Hansen, DTU Compute

Convergence and Non-Convergence of Algebraic Iterative Reconstruction Methods

Algebraic Iterative Reconstruction methods – such as ART (Kaczmarz), SART, and SIRT produce good results for underdetermined problems, and they can easily incorporate non-negativity and box constraints.
When AIR methods are implemented on GPU-accelerated systems with a focus on computational efficiency, different computational schemes are used for the forward projection and the backprojection. In the algebraic “language” of the AIR methods, this means that the backprojection matrix B is not the transpose AT of the forward projection matrix A. The use of B  AT has two consequences: the accuracy (compared to when using AT) deteriorates, and the iteration may fail to converge.
In this talk we illustrate these issues with recent theoretical and computational results, and we present a novel approach to “fixing” the non-convergence with only a small computational overhead.

This is joint work with Tommy Elfving from Linköping University, Michiel Hochstenbach from TU Eindhoven, as well as Yiqiu Dong and Nicolai Riis from DTU Compute.

• T. Elfving and P. C. Hansen, Unmatched projector/backprojector pairs: perturbation and convergence analysis, SIAM J. Sci. Comput., 40 (2018), pp. A573–A591, doi: 10.1137/17M1133828.
• Y. Dong, P. C. Hansen, M. E. Hochstenbach, and N. A. B. Riis, Fixing Nonconvergence of algebraic iterative reconstruction methods with an unmatched backprojector; submitted to SIAM J. Sci. Comput.

11:35 Viktor Nikitin, Lund University

Fast reconstruction in dynamic tomography

12:10 → 12:30 plenary discsussion: Initiation to discussions

12:10 Brainstorming on themes to discuss in groups in the afternoon

12:30 → 13:30 lunch at LINXS

13:30 → 15:15 talks with tutorials / hands-on: tools in phase retrieval and tomography

13:30 Daniel Pelt, CWI Amsterdam

Improving Tomographic Reconstruction and Analysis Using Mixed-Scale Dense Convolutional Neural Networks

In tomography, acquired projection data are often limited in one or more ways due to unavoidable experimental constraints, leading to inaccurate images. Using machine learning to improve image quality in tomography is a recently proposed solution, for which promising results have been shown. In this talk, I will present the use of Mixed-Scale Dense convolutional neural networks to improve tomographic reconstruction from (severely) limited data, and present a new software package for training and applying such networks in practice.

14:05 Jonas Adler, KTH Stockholm

ODL for Machine learning based tomographic image reconstruction

ODL is a python library for inverse problems developed jointly by several research groups and companies. We introduce ODL and how it can be used for variational reconstruction in inverse problems and further demonstrate how ODL can be used as a building block in learned iterative reconstruction methods and for learned optimization.

14:40 Doga Gursoy

TomoPy and related tools

15:15 → 15:30 fika

15:30 → 17:00 discussion corners: (A) phasing - (B) tomography - (C) deep learning

17:00 → 18:00 plenary discsussion: report from groups and conclusions

18:00 → 19:30 sandwich dinner and refreshment at LINXS

19:30 → 19:35 The End