C11 - Fresnel wavelets for coherent diffractive imaging

Within this funding period we aim to analyze the convergence of our phase retrieval algorithms using sparsity in shearlet frames and to extend them to 3D data in Fresnel and Fraunhofer regime.
We are furthermore interested in deriving new sparsity constraints based on adaptive wavelet frames instead of directional (but non-adaptive) shearlets with a focus on faster reconstruction algorithms in the 3D case. The obtained approach of incorporating wavelet-frame sparsity constraints into relaxed averaged alternating reflection algorithms will be compared with the phase reconstruction using a regularization approach in cooperation with projects C02 (Hohage/Luke) and C09 (Hohage). The wavelet frame sparsity constraints will be also applied to derive a new regularized object reconstruction method based on the transport of intensity equation in collaboration with project C01 (Salditt).

Members of this project:

Prof. Dr. Gerlind Plonka-Hoch
Dr. Stefan Loock
Jakob Geppert

Associated members of this project:


Geppert, J., Krahmer, F. and Stöger, D. (2019)
Sparse Power Factorization: Balancing peakiness and sample complexity
Advances in Computational Mathematics, 45(3) 1711–1728, 2019

Beinert, R. and Plonka, G. (2018)
Enforcing uniqueness in one-dimensional phase retrieval by additional signal information in time domain
Applied and Computational Harmonic Analysis, 45: 505-525

Beinert, R. and Plonka, G. (2017)
Sparse phase retrieval of structured signals by Prony’s method
PAMM · Proc. Appl. Math. Mech., 17: 829 – 830, DOI:10.1002/pamm.201710382

Beinert, R. (2017)
One-dimensional phase retrieval with additional interference measurements
Results Math.: 72(1-2)

Beinert, R. (2017)
Non-negativity constraints in the one-dimensional dicrete-time phase retrieval problem
Information and Inference: A Journal of the IMA,, 6: 213-224

Beinert, R. (2017)
Ambiguities in one-dimensional phase retrieval from magnitudes of a linear canonical transform
ZAMM - Z. Angew. Math. Mech., 97(9): 1078–1082

Beinert, R. and Plonka, G. (2017)
Sparse Phase Retrieval of One-Dimensional Signals by Prony's Method
Front. Appl. Math. Stat.: 3:5, DOI:10.3389/fams.2017.00005

Loock, S. and Plonka, G. (2016)
Iterative Phase Retrieval with Sparsity Constraints
PAMM, 16(1): 835-836, DOI:10.1002/pamm.201610406

Pein, A., Loock, S., Plonka, G. and Salditt, T. (2016)
Using sparsity information for iterative phase retrieval in x-ray propagation imaging
Optics Express, 24(8): pp. 8332-8343, DOI:10.1364/OE.24.008332

Beinert, R. and Plonka, G. (2015)
Ambiguities in one‐dimensional phase retrieval of structured functions
PAMM - Proc. Appl. Math. Mech, 15: 653-654, DOI:10.1002/pamm.201510316

Beinert, R. and Plonka, G. (2015)
Ambiguities in One-Dimensional Discrete Phase Retrieval from Fourier Magnitudes
J Fourier Anal Appl, DOI:10.1007/s00041-015-9405-2

Loock, S. and Plonka, G. (2014)
Phase retrieval for Fresnel measurements using a shearlet sparsity constraint
Inverse Probl., 30(5): 055005, DOI:10.1088/0266-5611/30/5/055005