SFB 755 - Nanoscale Photonic Imaging

A04 - Statistical multi-scale analysis for photonic imaging: from modeling to algorithms

Statistical multi-scale analysis for photonic imaging: from modeling to algorithms
In this project we aim for the development, statistical analysis and computation of statistical variational multiscale estimators which are specifically tailored to deconvolution in nanoscale biophotonic microscopy imaging. A special emphasis is the development of inferential methods for these techniques in Poisson and sub-Poisson models as well as on the development and implementation of first-order, forward-backward algorithms to compute these.

Members of this project:

Prof. Ph.D. Russell Luke
Prof. Dr. Axel Munk
Dr. Yurii Malitskyi
Claudia König

Associated members of this project:
PD Dr. Timo Aspelmeier
Dr. Frank Werner


Publications:

König, C., Munk, A. and Werner, F. (2019)
Multidimensional multiscale scanning in Exponential Families: Limit theory and statistical consequences
arXiv:1802.07995

Álamo, M., Li, H. and Munk, A. (A04)
Frame-constrained Total Variation Regularization for White Noise Regression
arXiv:1807.02038

Álamo, M. del and Munk, A. (2019)
Total variation multiscale estimators for linear inverse problems
DOI:1905.08515

Luke, R. D. and Malitsky, Y. (2018)
Block-coordinate primal-dual method for the nonsmooth minimization over linear constraints
DOI:arXiv:1801.04782

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

Luke, D. R. and Shefi, R. (2017)
A Globally Linearly Convergent Method for Pointwise Quadratically Supportable Convex-Concave Saddle Point Problems
Math. Anal. and Appl., DOI:10.1016/j.jmaa.2017.02.068

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

Munk, A. (2017)
Using nanostatistics to determine the functions of cells at a molecular level
Research Features Magazine: 56-57

Charitha, C., Dutta, J. and Luke, R.D. (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

Aspelmeier, T., Charitha, C. and Luke, D. (2016)
Local Linear Convergence of the ADMM/Douglas--Rachford Algorithms without Strong Convexity and Application to Statistical Imaging
SIAM J. Imaging Sciences

HUCKEMANN, S., KIM, K.-R., MUNK, A., REHFELDT, F., SOMMERFELD, M., WEICKERT, J. and WOLLNIK, C. (2016)
The circular SiZer, inferred persistence of shape parameters and application to early stem cell differentiation
Bernoulli, 22(4): 2113?2142, DOI:10.3150/15-BEJ722

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

Hartmann, A., Huckemann, S., Dannemann, J., Laitenberger, O., Geisler, C., Egner, A. and Munk, A. (2015)
Drift estimation in sparse sequential dynamic imaging, with application to nanoscale fluorescence microscopy
Journal of the Royal Statistical Society: Series B (Statistical Methodology), DOI:doi: 10.1111/rssb.12128

Peter, P., Weickert, J., Munk, A., Krivobokova, T. and Li, H. (2015)
Justifying Tensor-Driven Diffusion from Structure-Adaptive Statistics of Natural Images
Energy Minimization Methods in Computer Vision and Pattern Recognition,,(Volume 8932 of the series Lecture Notes in Computer Science): 263-277

Haltmeier, M. and Munk, A. (2014)
Extreme value analysis of empirical frame coefficients and implications for denoising by soft-thresholding
ELSEVIER, 36(3): 434-460, DOI:10.1016/j.acha.2013.07.004

Bauschke, H. H., Luke, D. R., Phan, H. M. and Wang, X. (2014)
Restricted normal cones and sparsity optimization with affine constraints
Foundations of Computational Mathematicsopen access,, 14(1): 63, DOI:10.1007/s10208-013-9161-0

Charitha, C., Dutta, J. and Lalitha, C. S. (2014)
Gap functions for vector variational inequalities
OptimizationTaylor & Francis,(March): 1-22, DOI:10.1080/02331934.2014.888556

Hafi, N., Grunwald, M., van den Heuvel, L. S., Aspelmeier, T., Chen, J.-H., Zagrebelsky, M., Schütte, O. M., Steinem, C., Korte, M., Munk, A. and Walla, P. J. (2014)
Fluorescence nanoscopy by polarization modulation and polarization angle narrowing.
Nat. Methods, 11(5): 579-84, DOI:10.1038/nmeth.2919

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

Yalunin, S. V., Herink, G., Solli, D. R., Krüger, M., Hommelhoff, P., Diehn, M., Munk, A. and Ropers, C. (2013)
Field localization and rescattering in tip-enhanced photoemission
Ann. Phys., 525(1-2): L12-L18, DOI:10.1002/andp.201200224

Bauschke, H. H., Luke, D. R., Phan, H. M. and Wang, X. (2013)
Restricted Normal Cones and the Method of Alternating Projections: Theory
Set-Valued Var. Anal., 21(3): 431-473, DOI:10.1007/s11228-013-0239-2

Bauschke, H. H., Luke, D. R., Phan, H. M. and Wang, X. (2013)
Restricted Normal Cones and the Method of Alternating Projections: Applications
Set-Valued Var. Anal., 21(3): 475-501, DOI:10.1007/s11228-013-0238-3

Frick, K. and Marnitz, P. (2012)
A Statistical Multiresolution Strategy for Image Reconstruction
Bruckstein, A. M., ter Haar Romeny, B. M., Bronstein, A. M. & Bronstein, M. M.Scale Space and Variational Methods in Computer VisionSpringer Berlin Heidelberg,: 74-85, DOI:10.1007/978-3-642-24785-9_7

Frick, K., Marnitz, P. and Munk, A. (2012)
Statistical multiresolution Dantzig estimation in imaging: Fundamental concepts and algorithmic framework
Electron. J. Stat., 6: 231-268, DOI:10.1214/12-EJS671

Frick, K., Marnitz, P. and Munk, A. (2012)
Shape-constrained regularization by statistical multiresolution for inverse problems: asymptotic analysis
Inverse Probl., 28(6): 065006, DOI:10.1088/0266-5611/28/6/065006

Frick, K., Marnitz, P. and Munk, A. (2012)
Statistical Multiresolution Estimation for Variational Imaging: With an Application in Poisson-Biophotonics
J. Math. Imaging Vis., 46(3): 370-387, DOI:10.1007/s10851-012-0368-5

Haltmeier, M. and Munk, A. (2012)
Extreme Value Analysis of Empirical Frame Coefficients and Implications for Denoising by Soft-Thresholding
Appl. Comput. Harmon. Anal., 36: 434, DOI:10.1016/j.acha.2013.07.004

Hotz, T., Marnitz, P., Stichtenoth, R., Davies, L., Kabluchko, Z. and Munk, A. (2011)
Locally adaptive image denoising by a statistical multiresolution criterion
Comput. Stat. Data Anal.Elsevier B.V.,, 56(3): 543-558, DOI:10.1016/j.csda.2011.08.018

Munk, A. and Pricop, M. (2010)
On the self-regularization property of the EM algorithm for Poisson inverse problems
Kneib, T. & Tutz, G.Statistical Modelling and Regression StructuresPhysica-Verlag HD,: 431-448, DOI:10.1007/978-3-7908-2413-123

Bissantz, N., Claeskens, G., Holzmann, H. and Munk, A. (2009)
Testing for Lack of Fit in Inverse Regression: With Applications to Biophotonic Imaging
Journal of the Royal Statistical Society. Series B, 71(1): 25-48

Lakomek, N. A., Walter, K. F. A., Farès, C., Lange, O. F., de Groot, B. L., Grubmüller, H., Brüschweiler, R., Munk, A., Becker, S., Meiler, J. and Griesinger, C. (2008)
Self-consistent residual dipolar coupling based model-free analysis for the robust determination of nanosecond to microsecond protein dynamics
Journal of Biomolecular NMR, 41: 139-155, DOI:10.1007/s10858-008-9244-4

Bissantz, N., Mair, B. A. and Munk, A. (2008)
A statistical stopping rule for MLEM reconstructions in PET
IEEE Nuclear Science Symposium Conference Record: 4198-4200, DOI:10.1109/NSSMIC.2008.4774207