Examples: Ptychographic Imaging
By combining diffraction with microscopy and the computational power of GPUs, one can quickly turn high throughput "imaging by diffraction" techniques into the sharpest images ever produced. Every scanning microscope can now add a parallel detector, and every diffraction imaging instrument can add a scanning stage to take advantage of this disruptive technique. To sustain high throughput processing (~>TB/h) the CAMERA collaboration has recently released a software suite for high throughput real time ptychographic data analysis which is freely available* and open for collaborative development.
SHARP real-time robust ptychographic imaging
Joint work with B Daurer, F Maia (NERSC/Uppsala),
Convergence theory, Scalable Algorithms and Lens Design
Joint work with Y-C Tu (Mathematics, Princeton), H-T Wu (Mathematics, Toronto)
The ability to reconstruct a sample from its diffraction pattern has been a standing issue for over 100 years. We provide necessary and sufficient conditions for the global convergence to a unique solution for any object of interest under general experimental conditions such as ptychography. Additionally, we show how to scale the algorithms by exploiting synchronization and connection graph Laplacians to handle the big imaging data in the coming new light source era. Finally, we propose new lens design to increase resolution, robustness and information throughput.
 Alternating Projection, Ptychographic Imaging and Phase Synchronization, S. Marchesini, Y-C Tu, H-T Wu, [http://arxiv.org/abs/1402.0550].
Robust ptychography: algorithms for noisy data and experimental perturbations in high dimensions
Joint work with H-T Wu (Mathematics, Stanford), C. Yang, A. Schirotzek (LBL)
Diffraction measurements from neighboring regions are related to each other by the illumination geometry. This motivates us to consider augmented projections and synchronization strategies aimed at organizing local information in a global way. We have developed numerical solvers to handle situations when sample, illumination function, incoherent effects, as well as positions, are all unknown parameters in high dimensions based on spectral methods, conjugate gradient, Newton , and augmented Lagrangian  methods, some of which are in production at 4 microscopes at the Advanced Light Source.
S. M. et al, "Augmented projections for ptychographic imaging." Inverse Problems 29.11 (2013): 115009.
Low Latency Ptychography Imaging by High Performance Computing
Joint work with C. Yang (LBL), Filipe Maia, B Daurer (NERSC/Uppsala), , Z. Wen (Mathematics, Shanghai)
With the ever increasing brightness of x-ray sources, it is now possible to see what no one was ever able to see before: macroscopic specimens in 3D at wavelength resolution. By combining diffraction with microscopy and the computational power of GPUs, one can quickly turn high throughput "imaging by diffraction" techniques into the sharpest images ever produced. To sustain high throughput processing (~>TB/h) we use a small cluster and developed distributed code that exhibit strong scaling over dozens of nodes. In the near future, low latency feedback will be made possible by streaming detector packets through our distributed machine directly into the analysis backend computer.
Wen, Z, et al. "Alternating direction methods for classical and ptychographic phase retrieval." Inv. Problems 28.11 (2012) 115010.
Yang, C, et al. "Iterative algorithms for ptychographic phase retrieval." Contemporary Mathematics, to appear, arXiv preprint arXiv:1105.5628 (2011).
Presentation by F. Maia at Ptychography 2013( real_time_ptychography.pdf) :
A range of applications was discussed in a recent workshop held at Berkeley Lab
Jordi Cabana: Battery research and the opportunities for new x-ray techniques,
R. Ritchie: Bone and high strength nano-composite materials
P. Monteiro: Green Concrete and Sustainable Construction
D. DePaulo: nanoscale structure of rocks related to carbon sequestration
T. Russell: Fronteers in soft matter: "Can X-ray Scattering and Microscopy Help?",
Brian Collins: Organic Devices: "An Application in Need of New Tools"
R. Segalman: Chemical structure of 3d polymeric materials for energy application
R. Ramesh: multiferroic nanomaterials
Hyperspectral Ptycho-tomography Coherent scattering and Microscopy facility. Soon open to general users for scientific discovery.
Dedicated ptychography beamline: https://sites.google.com/a/lbl.gov/cosmic/home