GAMM2025

Session

S21: Mathematical signal and image processing

S21

9 Apr 2025, 08:30

Lecture and Conference Centre

Conveners

S21: Mathematical signal and image processing: S21.01

• Oleh Melnyk

S21: Mathematical signal and image processing: S21.02

• Stefania Petra

S21: Mathematical signal and image processing: S21.03

• Stefania Petra

S21: Mathematical signal and image processing: S21.04

• Benjamin Berkels

Description

Over the last decade mathematics has become the cornerstone in Signal and Image processing ranging from various methods for signal reconstruction to modelling of imaging modalities over its classical disciplines compression, denoising, segmentation, and registration to feature extraction. The used methodologies include such diverse fields as harmonic analysis, inverse problems, variational analysis, mathematical statistics, partial differential equations, optimization, approximation theory and sampling theory. The aim of this section is to foster interdisciplinary collaboration and the development of new directions in mathematical signal and image processing spawned from the interaction of various mathematical communities.

481. Duality in nonlinear eigenproblems

Jonathan Laubmann

09/04/2025, 08:30

Nonlinear eigenproblems are an interesting tool for image processing and clustering tasks in data science. Recent approaches aim to determine eigenvectors, and in particular ground states, of nonlinear operators via respective energy functionals such as the total variation regularization. Typically, these eigenvectors are numerically approximated using gradient flows to minimize a nonlinear...

482. Adjointfree Estimation of Operator Norms Do we need the Adjoint to Estimate Operator Norms?

Felix Schneppe

09/04/2025, 09:10

In this talk, we address the challenge of determining the norm of a linear operator solely by evaluating it. This problem naturally arises whenever the adjoint is not known and cannot be attained. After giving an overview of algorithms fitted to this problem, we propose an algorithm that employs a semi-stochastic approach to iteratively refine the estimate, achieving almost sure convergence to...

483. Hyperspectral Image denoising via Low-rank Tucker decomposition with Subspace Implicit Neural Representation

Jiangjun Peng

09/04/2025, 16:30

Hyperspectral image (HSI) denoising is an important preprocessing step for downstream applications. Fully characterizing the spatial-spectral priors of HSI is crucial for denoising tasks. In recent years, denoising methods based on low-rank subspaces have garnered widespread attention. In the low-rank matrix factorization framework, the restoration of HSI can be formulated as a task of...

484. Denoising Hyperbolic-Valued Data by Relaxed Regularizations

Jonas Bresch

09/04/2025, 16:50

We introduce a novel relaxation strategy for denoising hyperbolic-valued data. The main challenge is here the non-convexity of the hyperbolic sheet. Instead of considering the denoising problem directly on the hyperbolic space, we exploit the Euclidean embedding and encode the hyperbolic sheet using a novel matrix representation. For denoising, we employ the Euclidean Tikhonov and total...

485. Riemannian Patch Assignment Gradient Flows

Daniel Gonzalez-Alvarado

09/04/2025, 17:10

This paper introduces patch assignment flows for metric data labeling on graphs. Labelings are determined by regularizing initial local labelings through the dynamic interaction of both labels and label assignments across the graph, entirely encoded by a dictionary of competing labeled patches and mediated by patch assignment variables. Maximal consistency of patch assignments is achieved by...

486. Information Geometry of Exponentiated Gradient: Convergence beyond L-Smoothness

Yara Elshiaty

09/04/2025, 17:30

We study the minimization of smooth, possibly nonconvex functions over the positive orthant, a key setting in Poisson inverse problems, using the exponentiated gradient (EG) method. Interpreting EG as Riemannian gradient descent (RGD) with the e-Exp map from information geometry as a retraction, we prove global convergence under weak assumptions -- without the need for L-smoothness -- and...

487. Variational exit wave reconstruction - From classical approaches to deep unfolding

Benjamin Berkels

10/04/2025, 08:30

We revisit the so-called exit wave reconstruction problem in the variational setting. Here, exit wave reconstruction means to reconstruct the complex-valued electron wave in a transmission electron microscope (TEM) right before it passes the objective lens, i.e., the exit wave, from a focus series of real-valued TEM images. This is a non-linear inverse problem that is a variant of the well...

488. Towards a super-resolution theory for infinite-width shallow neural networks

Marcello Carioni

10/04/2025, 09:10

In this talk, I will present recent results regarding super-resolution properties of infinite-width shallow neural networks.

It is well-known that the training of shallow neural networks can be convexified by lifting the weights space to measures defined on a sphere. This gives rise to a convex optimization problem on measures, that, depending on the chosen activation function, exhibits...

489. Pattern-Generating Reaction-Diffusion Systems for Texture Processing: Towards Generative Texture Descriptors

Martin Welk

10/04/2025, 09:30

Spontaneous formation of patterns by reaction-diffusion systems was discovered by Alan Turing in the 1950s and has been investigated from many different angles since then. We are interested in utilising this phenomenon in the context of texture analysis and synthesis. As a first task, we investigate the estimation of parameters of a pattern-generating reaction-diffusion system of Gray-Scott...

490. Bundle Scale Spaces and Local Gauge Symmetries for Graph Networks

Jonas Cassel

10/04/2025, 09:50

We introduce a class of processing architectures for node features on a graph, that are equivariant with respect to a local G-action, where G is a group. A local group action acts on feature vectors at graph nodes via group elements, which need not be equal for all graph nodes. Local symmetries are already considered in several works in the context of data science, ranging from color image...

491. Multilevel Optimization: Geometric Coarse Models and Convergence Analysis

Ferdinand-Joseph Vanmaele

10/04/2025, 10:10

We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a descent direction for the fine-grid objective using fewer variables. Unlike common algebraic approaches, we assume the objective function and its gradient can...

492. Covariance Matrix Estimation for Massive MIMO

Laura Paul

10/04/2025, 14:00

Massive multiple-input multiple-output (MIMO) communication systems are very promising for wireless communication and fifth generation (5G) cellular networks. In massive MIMO, a large number of antennas are employed at the base station (BS), which provides a high degree of spatial freedom and enables the BS to simultaneously communicate with multiple user terminals. Due to the limited angular...

493. Time-Harmonic Optical Flow with Applications in Elastography

Oleh Melnyk

10/04/2025, 14:20

In this talk, we propose mathematical models for reconstructing the optical flow in time-harmonic elastography. In this image acquisition technique, the object undergoes a special time-harmonic oscillation with known frequency so that only the spatially varying amplitude of the velocity field has to be determined. This allows for a simpler multi-frame optical flow analysis using Fourier...

494. Reconstructing Missing Fourier Data in MRI: Exploring GRAPPA and Subsampling Strategies in the Fourier Domain

Anahita Riahi

10/04/2025, 14:40

In applications such as Magnetic Resonance Imaging (MRI), data are acquired in the Fourier domain and to accelerate imaging, a subsample of the discrete Fourier data is often taken. In order to recover the image, we need to reconstruct the missing Fourier data and then apply the discrete inverse Fourier transform. However, reconstructing missing data in the Fourier Space poses significant...

495. Automated Adjustment of the Focussing Optics of Free-electron Lasers

Janina Schmidt

10/04/2025, 15:00

FLASH is a free-electron laser capable of emitting femto second short pulses of light in the X-ray spectrum. Before the beam is used in experiments, it should be focused. This is done by a Kirkpatrick-Baez mirror system which consists of two mirrors that can be bent, rotated, and translated. At the moment this mirror system has to be tuned by hand before each experiment, which is very...

496. Adaptive Bregman–Kaczmarz: an approach to solve linear inverse problems with independent noise exactly

Lionel Tondji

10/04/2025, 15:20

We consider the block Bregman–Kaczmarz method for finite dimensional linear inverse problems. The block Bregman–Kaczmarz method uses blocks of the linear system and performs iterative steps with these blocks only. We assume a noise model that we call independent noise, i.e. each time the method performs a step for some block, one obtains a noisy sample of the respective part of the right-hand...

497. Density estimation for broken random samples

Hancheng Bi

10/04/2025, 15:40

Consider the broken random sample problem introduced by DeGroot, Feder, and Gole (1971 Ann. Math. Statist.): In each observation, a random sample of M point pairs ((Xᵢ,Yᵢ))ᵢ₌₁ᴹ is drawn from a joint distribution with density f(x,y). Assume we can only observe (Xᵢ)ᵢ₌₁ᴹ and (Yᵢ)ᵢ₌₁ᴹ separately, i.e.~the pairing information is lost. We are interested in estimating f given N i.i.d.~observations....