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Convergence properties of ePIE and stochastic gradient methods for blind ptychography
We consider blind ptychography, an imaging technique which aims to reconstruct an object of interest from a set of its diffraction …
Oleh Melnyk
DOI
Time-Harmonic Optical Flow with Applications in Elastography

In this paper, we propose mathematical models for reconstructing the optical flow in time-harmonic elastography. In this image …

Oleh Melnyk, Michael Quellmalz, Gabriele Steidl, Noah Jaitner, Jakob Jordan, Ingolf Sack
DOI
Sparse additive function decompositions facing basis transforms
High-dimensional real-world systems can often be well characterized by a small number of simultaneous low-complexity interactions. The …
Fatima Antarou Ba, Oleh Melnyk, Christian Wald, Gabriele Steidl
DOI
Background Removal for Ptychography via Wigner Distribution Deconvolution
Ptychography is a computational imaging technique that aims to reconstruct the object of interest from a set of diffraction patterns. …
Oleh Melnyk, Patricia Römer
DOI
Image Recovery for Blind Polychromatic Ptychography
Ptychography is a lensless imaging technique, which considers reconstruction from a set of far-field diffraction patterns obtained by …
Frank Filbir, Oleh Melnyk
DOI
Inverse Multislice Ptychography by Layer-wise Optimisation and Sparse Matrix Decomposition
We propose algorithms based on an optimisation method for inverse multislice ptychography in, e.g. electron microscopy. The multislice …
Arya Bangun, Oleh Melnyk, Benjamin März, Benedikt Diederichs, Alexander Clausen, Dieter Weber, Frank Filbir, Knut Müller-Caspary
DOI
On connections between Amplitude Flow and Error Reduction for phase retrieval and ptychography
In this paper, we consider two iterative algorithms for the phase retrieval problem: the well-known Error Reduction method and the …
Oleh Melnyk
DOI
On the robustness of noise-blind low-rank recovery from rank-one measurements

We prove new results about the robustness of well-known convex noise-blind optimization formulations for the reconstruction of low-rank …

Felix Krahmer, Christian Kümmerle, Oleh Melnyk
DOI
On Recovery Guarantees for Angular Synchronization
The angular synchronization problem of estimating a set of unknown angles from their known noisy pairwise differences arises in various …
Frank Filbir, Felix Krahmer, Oleh Melnyk
DOI
Well-conditioned ptychographic imaging via lost subspace completion
Ptychography,aspecialcaseofthephaseretrievalproblem,isapopularmethod in modern imaging. Its measurements are based on the shifts of a …
Anton Forstner, Felix Krahmer, Oleh Melnyk, Nada Sissouno
DOI