SFB 755 - Nanoscale Photonic Imaging

C02 - Inverse scattering problems without phase

This project concerns the mathematical theory of, and algorithms for inverse problems in x-ray physics involving measurements of the amplitude, but not the phase of the field. We treat these problems as nonlinear ill-posed operator equations or as non-convex optimization or feasibility problems. In particular, we will study tomographic phase contrast imaging and ptychography, exploiting the special structure of these problems to achieve close to optimal reconstruction within reasonable computation times.

Members of this project:

Prof. Thorsten Hohage
Prof. Ph.D. Russell Luke
M.Sc. Simon Maretzke
M.Sc. Anna-Lena Martins


Publications:

van Leeuwen, T., Maretzke, S. and J. Batenburg (2018)
Automatic alignment for three-dimensional tomographic reconstruction
Inverse Problems, 34(2)

Lauster, F., Luke, D. R. and Tam, M. K. (2017)
Symbolic Computation with Monotone Operators
Set Valued and Variational Analysis, DOI:10.1007/s11228-017-0418-7

Maretzke, S. and Hohage, T. (2017)
Stability Estimates for Linearized Near-Field Phase Retrieval in X-ray Phase Contrast Imaging
SIAM J. APPL. MATH, 77(2): 384-408, DOI:10.1137/16M1068170

Luke, D. R. (2017)
Phase Retrieval, What`s New?
SIAG/OPT Views and News, 25(1)

Charitha, C., Dutta, J. and R.D., L. (2016)
Lagrange multipliers, (exact) regularization and error bounds for monotone variational inequalities
Lagrange multipliers, (exact) regularization and error bounds for monotone variational inequalities, DOI:10.1007/s10107-016-1022-6

Luke, D. R. (2017)
Phase Retrieval, What?s New?
SIAG/OPT Views and News, 25(1)

König, C., WERNER, F. and Hohage, T. (2016)
CONVERGENCE RATES FOR EXPONENTIALLY ILL-POSED INVERSE PROBLEMS WITH IMPULSIVE NOISE
SIAM J. NUMER. ANAL
Society for Industrial and Applied Mathematics, 54(1): 341?360, DOI:10.1137/15M1022252

Maretzke S. and Bartels, M., Krenkel, M., Salditt, T. and Hohage, T. (2016)
Regularized Newton methods for x-ray phase contrast and general imaging problems
OPTICS EXPRESS, 24(6): 6490, DOI:10.1364/OE.24.006490

Hesse, R., Luke, D., Sabach, S. and Tam, M. (2015)
Proximal Heterogeneous Block Implicit-Explicit Method and Application to Blind Ptychographic Diffraction Imaging
SIAM J. on Imaging Science, 8(1): 426-457

Maretzke, S. (2015)
A uniqueness result for propagation-based phase contrast imaging from a single measurement
Inverse Problems, 31: 065003, DOI:http://dx.doi.org/10.1088/0266-5611/31/6/065003

Homann, C., Hohage, T., Hagemann, J., Robisch, A. and Salditt, T. (2015)
Validity of the empty-beam correction in near-field imaging
Phys. Rev. A, 91: 013821, DOI:10.1103/PhysRevA.91.013821

Hohage, T. and Le Louer, F. ()
A spectrally accurate method for the dielectric obstacle scattering problem and applications to the inverse problem
num.math.uni-goettingen.deInstitut für Numerische und Angewandte Mathematik,(19)

Homann, C., Hohage, T., Hagemann, J., Robisch, A. and Salditt, T. (2015)
Validity of the empty-beam correction in near-field imaging
Phys. Rev. A, 91: 013821, DOI:10.1103/PhysRevA.91.013821

Hagemann, J., Robisch, A. and Luke, D. (2014)
Reconstruction of wave front and object for inline holography from a set of detection planes
Opt. Express, 22(10): 195-202, DOI:10.1364/OE.22.011552

Hesse, R., Luke, D. R. and Neumann, P. (2014)
Alternating Projections and Douglas-Rachford for Sparse Affine Feasibility
IEEE Trans. Signal Process., 62(18): 4868-4881, DOI:10.1109/TSP.2014.2339801

Hesse, R., Luke, D. R., Sabach, S. and Tam, M. K. (2014)
Proximal Heterogeneous Block Input-Output Method and application to Blind Ptychographic Diffraction Imaging
arXiv: 1-32

Hohage, T. and Homann, C. (2014)
A Generalization of the Chambolle-Pock Algorithm to Banach Spaces with Applications to Inverse Problems
arXiv: 1

Maretzke, S. (2014)
A uniqueness result for propagation-based phase contrast imaging from a single measurement
arXiv: 1

Hesse, R. and Luke, D. R. (2013)
Nonconvex Notions of Regularity and Convergence of Fundamental Algorithms for Feasibility Problems
SIAM J. Optim.open access,, 23(4): 2397, DOI:10.1137/120902653

Hohage, T. and Werner, F. (2012)
Iteratively regularized Newton-type methods for general data misfit functionals and applications to Poisson data
Numer. Math.open access,, 123(4): 745-779, DOI:10.1007/s00211-012-0499-z

Kress, R. and Rundell, W. (2013)
Reconstruction of extended sources for the Helmholtz equation
Inverse Probl., 29(3): 035005, DOI:10.1088/0266-5611/29/3/035005

Luke, D. R. (2012)
Local linear convergence of approximate projections onto regularized sets
Nonlinear Anal. Theory, Methods Appl., 75(3): 1531-1546, DOI:10.1016/j.na.2011.08.027

Hassen, M. F. B., Ivanyshyn, O. and Sini, M. (2010)
Three-dimensional acoustic scattering by complex obstacles: the accuracy issue
Inverse Problems, 26: 105008, DOI:10.1088/0266-5611/26/10/105008

Ivanyshyn, O. and Kress, R. (2011)
Inverse scattering for surface impedance from phase-less far field data
Journal of Computational Physics, 230(9): 3443-3452, DOI:10.1016/j.jcp.2011.01.038

Ivanyshyn, O. and Kress, R. (2010)
Identification of sound-soft 3D obstacles from phaseless data
Inverse Problems and Imaging, 4: 131-149, DOI:10.3934/ipi.2010.4.131

Ivanyshyn, O., Kress, R. and Serranho, P. (2010)
Huygens' principle and iterative methods in inverse obstacle scattering
Advances in Computational Mathematics, 33: 413-429, DOI:10.1007/s10444-009-9135-6

Ivanyshyn, O. (2007)
Shape reconstruction of acoustic obstacles from the modulus of the far field pattern
Inverse Problems and Imaging, 1: 609-622, DOI:10.3934/ipi.2007.1.609