17 citations · 50 across the 14 of their papers we have counts for
14 papers
Stochastic Zeroth-Order Method for Computing Generalized Rayleigh Quotients
Jonas Bresch, Oleh Melnyk, Martin Schoen +1
The maximization of the (generalized) Rayleigh quotient is a central problem in numerical linear algebra. Conventional algorithms for its computation typically rely on matrix-adjoi…
Unsupervised Ground Metric Learning
Janis Auffenberg, Jonas Bresch, Oleh Melnyk +1
Data classification without access to labeled samples remains a challenging problem. It usually depends on an appropriately chosen distance between features, a topic addressed in m…
Phasebook: A Survey of Selected Open Problems in Phase Retrieval
Marc Allain, Selin Aslan, Wim Coene +13
Phase retrieval is an inverse problem that, on one hand, is crucial in many applications across imaging and physics, and, on the other hand, leads to deep research questions in the…
Eigenstructure Analysis of Bloch Wave and Multislice Formulations for Dynamical Scattering in Transmission Electron Microscopy
Arya Bangun, Oleh Melnyk, Benjamin März
We investigate the eigenstructure of matrix formulations used for modeling scattering processes within materials in transmission electron microscopy. Dynamical scattering is crucia…
Time-Harmonic Optical Flow with Applications in Elastography
Oleh Melnyk, Michael Quellmalz, Gabriele Steidl +3
In this paper, we propose mathematical models for reconstructing the optical flow in time-harmonic elastography. In this image acquisition technique, the object undergoes a special…
Sparse additive function decompositions facing basis transforms
Fatima Antarou Ba, Oleh Melnyk, Christian Wald +1
High-dimensional real-world systems can often be well characterized by a small number of simultaneous low-complexity interactions. The analysis of variance (ANOVA) decomposition an…
Background Denoising for Ptychography via Wigner Distribution Deconvolution
Oleh Melnyk, Patricia Römer
Ptychography is a computational imaging technique that aims to reconstruct the object of interest from a set of diffraction patterns. Each of these is obtained by a localized illum…
Convergence properties of gradient methods for blind ptychography
Oleh Melnyk
We consider blind ptychography, an imaging technique which aims to reconstruct an object of interest from a set of its diffraction patterns, each obtained by a local illumination.…
Stochastic Amplitude Flow for phase retrieval, its convergence and doppelgängers
Oleh Melnyk
In this paper, we focus on Stochastic Amplitude Flow (SAF) for phase retrieval, a stochastic gradient descent for the amplitude-based squared loss. While the convergence to a criti…
Image Recovery for Blind Polychromatic Ptychography
Frank Filbir, Oleh Melnyk
Ptychography is a lensless imaging technique, which considers reconstruction from a set of far-field diffraction patterns obtained by illuminating small overlapping regions of the…
Inverse Multislice Ptychography by Layer-wise Optimisation and Sparse Matrix Decomposition
Arya Bangun, Oleh Melnyk, Benjamin März +5
We propose algorithms based on an optimisation method for inverse multislice ptychography in, e.g. electron microscopy. The multislice method is widely used to model the interactio…
On the robustness of noise-blind low-rank recovery from rank-one measurements
Felix Krahmer, Christian Kümmerle, Oleh Melnyk
We prove new results about the robustness of well-known convex noise-blind optimization formulations for the reconstruction of low-rank matrices from underdetermined linear measure…
On recovery guarantees for angular synchronization
Frank Filbir, Felix Krahmer, Oleh Melnyk
The angular synchronization problem of estimating a set of unknown angles from their known noisy pairwise differences arises in various applications. It can be reformulated as a op…
Well conditioned ptychograpic imaging via lost subspace completion
Anton Forstner, Felix Krahmer, Oleh Melnyk +1
Ptychography, a special case of the phase retrieval problem, is a popular method in modern imaging. Its measurements are based on the shifts of a locally supported window function.…