Martin Genzel

Merantix Momentum

Generalized Additive Models (GAMs) have recently experienced a resurgence in popularity due to their interpretability, which arises from expressing the target value as a sum of non-linear transformations of the features. Despite the current enthusiasm for GAMs, their susceptibility to concurvity - i.e., (possibly non-linear) dependencies between th...

This work presents a novel deep-learning-based pipeline for the inverse problem of image deblurring, leveraging augmentation and pre-training with synthetic data. Our results build on our winning submission to the recent Helsinki Deblur Challenge 2021, whose goal was to explore the limits of state-of-the-art deblurring algorithms in a real-world da...

Countless signal processing applications include the reconstruction of signals from few indirect linear measurements. The design of effective measurement operators is typically constrained by the underlying hardware and physics, posing a challenging and often even discrete optimization task. While the potential of gradient-based learning via the un...

This work performs a non-asymptotic analysis of the generalized Lasso under the assumption of sub-exponential data. Our main results continue recent research on the benchmark case of (sub-)Gaussian sample distributions and thereby explore what conclusions are still valid when going beyond. While many statistical features remain unaffected (e.g., co...

This work is concerned with the following fundamental question in scientific machine learning: Can deep-learning-based methods solve noise-free inverse problems to near-perfect accuracy? Positive evidence is provided for the first time, focusing on a prototypical computed tomography (CT) setup. We demonstrate that an iterative end-to-end network sc...

Recent advances in quantized compressed sensing and high-dimensional estimation have shown that signal recovery is even feasible under strong nonlinear distortions in the observation process. An important characteristic of associated guarantees is uniformity, i.e., recovery succeeds for an entire class of structured signals with a fixed measurement...

Countless signal processing applications include the reconstruction of signals from few indirect linear measurements. The design of effective measurement operators is typically constrained by the underlying hardware and physics, posing a challenging and often even discrete optimization task. While the potential of gradient-based learning via the un...

In the past five years, deep learning methods have become state-of-the-art in solving various inverse problems. Before such approaches can find application in safety-critical fields, a verification of their reliability appears mandatory. Recent works have pointed out instabilities of deep neural networks for several image reconstruction tasks. In a...

Neural networks with random weights appear in a variety of machine learning applications, most prominently as the initialization of many deep learning algorithms and as a computationally cheap alternative to fully learned neural networks. In the present article we enhance the theoretical understanding of random neural nets by addressing the followi...

This report is dedicated to a short motivation and description of our contribution to the AAPM DL-Sparse-View CT Challenge (team name: "robust-and-stable"). The task is to recover breast model phantom images from limited view fanbeam measurements using data-driven reconstruction techniques. The challenge is distinctive in the sense that participant...

This paper investigates total variation minimization in one spatial dimension for the recovery of gradient-sparse signals from undersampled Gaussian measurements. Recently established bounds for the required sampling rate state that uniform recovery of all $s$-gradient-sparse signals in ${\mathbb{R}}^n$ is only possible with $m \gtrsim \sqrt{s n} \...

In the past five years, deep learning methods have become state-of-the-art in solving various inverse problems. Before such approaches can find application in safety-critical fields, a verification of their reliability appears mandatory. Recent works have pointed out instabilities of deep neural networks for several image reconstruction tasks. In a...

Recent advances in quantized compressed sensing and high-dimensional estimation have shown that signal recovery is even feasible under strong non-linear distortions in the observation process. An important characteristic of associated guarantees is uniformity, i.e., recovery succeeds for an entire class of structured signals with a fixed measuremen...

This paper investigates total variation minimization in one spatial dimension for the recovery of gradient-sparse signals from undersampled Gaussian measurements. Recently established bounds for the required sampling rate state that uniform recovery of all $s$-gradient-sparse signals in $\mathbb{R}^n$ is only possible with $m \gtrsim \sqrt{s n} \cd...

This work theoretically studies the problem of estimating a structured high-dimensional signal $\boldsymbol{x}_0 \in{\mathbb{R}}^n$ from noisy $1$-bit Gaussian measurements. Our recovery approach is based on a simple convex program which uses the hinge loss function as data fidelity term. While such a risk minimization strategy is very natural to l...

EDDIDAT is a MATLAB-based graphical user interface for the convenient and versatile analysis of energy-dispersive diffraction data obtained at laboratory and synchrotron sources. The main focus of EDDIDAT up to now has been on the analysis of residual stresses, but it can also be used to prepare measurement data for subsequent phase analysis or ana...

This work performs a non-asymptotic analysis of the (constrained) generalized Lasso under the assumption of sub-exponential data. Our main results continue recent research on the benchmark case of sub-Gaussian sample distributions and thereby explore what conclusions are still valid when going beyond. While many statistical features of the generali...

This paper investigates total variation minimization in one spatial dimension for the recovery of gradient-sparse signals from undersampled Gaussian measurements. Recently established bounds for the required sampling rate state that uniform recovery of all $s$-gradient-sparse signals in $\mathbb{R}^n$ is only possible with $m \gtrsim \sqrt{s n} \cd...

We study the estimation capacity of the generalized Lasso, i.e., least squares minimization combined with a (convex) structural constraint. While Lasso-type estimators were originally designed for noisy linear regression problems, it has recently turned out that they are in fact robust against various types of model uncertainties and misspecificati...

This work theoretically studies the problem of estimating a structured high-dimensional signal $x_0 \in \mathbb{R}^n$ from noisy $1$-bit Gaussian measurements. Our recovery approach is based on a simple convex program which uses the hinge loss function as data fidelity term. While such a risk minimization strategy is very natural to learn binary ou...

This paper investigates the problem of signal estimation from undersampled noisy sub-Gaussian measurements under the assumption of a cosparse model. Based on generalized notions of sparsity, we derive novel recovery guarantees for the L1-analysis basis pursuit, enabling highly accurate predictions of its sample complexity. The corresponding bounds...

This work deals with the problem of distributed data acquisition under non-linear communication constraints. More specifically, we consider a model setup where $M$ distributed nodes take individual measurements of an unknown structured source vector $x_0 \in \mathbb{R}^n$, communicating their readings simultaneously to a central receiver. Since thi...

Background: High-throughput proteomics techniques, such as mass spectrometry (MS)-based approaches, produce very high-dimensional data-sets. In a clinical setting one is often interested in how mass spectra differ between patients of different classes, for example spectra from healthy patients vs. spectra from patients having a particular disease....

In this paper, we study the challenge of feature selection based on a relatively small collection of sample pairs $\{(x_i, y_i)\}_{1 \leq i \leq m}$. The observations $y_i \in \mathbb{R}$ are thereby supposed to follow a noisy single-index model, depending on a certain set of signal variables. A major difficulty is that these variables usually cann...

In this paper, we study the issue of estimating a structured signal x_0 in R^n from non-linear and noisy Gaussian observations. Supposing that x_0 is contained in a certain convex subset K of R^n , we prove that accurate recovery is already feasible if the number of observations exceeds the effective dimension of K, which is a common measure for th...

The modified stress scanning method [Meixner, Fuss, Klaus & Genzel (2015). J. Appl. Cryst.48, 1451–1461] is experimentally implemented for the analysis of near-surface residual stress depth distributions that are strongly inhomogeneous. The suggested procedure is validated by analyzing the very steep in-plane residual stress depth profile of a shot...

Exploiting the advantages of energy-dispersive synchrotron diffraction, a method for the determination of strongly inhomogeneous residual stress depth gradients is developed, which is an enhancement of the stress scanning technique. For this purpose, simulations on the basis of a very steep residual stress depth profile are performed, and it is sho...

Recently introduced inpainting algorithms using a combination of applied harmonic analysis and compressed sensing have turned out to be very successful. One key ingredient is a carefully chosen representation system which provides (optimally) sparse approximations of the original image. Due to the common assumption that images are typically governe...

A method for the evaluation of strongly inhomogeneous residual stress fields in the near-surface region of polycrystalline materials is introduced, which exploits the full information content contained in energy-dispersive (ED) diffraction patterns. The macro-stress-induced diffraction line shifts ΔEψhkl observed in ED sin²ψ measurements are descri...

The paper deals with methods for X-ray stress analysis (XSA), which allow for the evaluation of near surface in-plane residual stress gradients sigma(parallel to)(Or) and sigma parallel to(z) in the LAPLACE- and the real space, respectively. Since the 'robustness' of residual stress gradient analysis strongly depends on both, the quality of the mea...