Syftet med seminarierna är att sprida kunskap om forskning med starka kopplingar till matematik. Detta inbegriper tillämpningar som involverar matematiska frågeställningar, tvärvetenskapliga forskningsproblem, samt annan forskning med inslag av matematik. Vi bjuder in personer från olika företag och universitetsinstitutioner för att diskutera utmaningar av tvärvetenskaplig karaktär.
Seminarierna som oftast hålls på engelska är öppna för allmänheten och alla intresserade är välkomna!
Kommande seminarier
Måndag 6 oktober 2025, 13.15-15.00, Minisymposium on Imaging
Lokal: , Campus Valla
Talare: Jan Rolfes, MAI
Titel: Utilizing Material Properties in the 3D Reconstruction of Functional Materials via Nanotomography
Sammanfattning: Nanotomography techniques such as electron tomography (ET) and nano X-ray computed tomography (nano-CT) allow high-resolution 3D imaging of functional materials (e.g. catalyst supports, battery electrodes or photonic crystals) and the determination of important material properties such as particle and pore size, position and interconnectivity, or chemical composition.
However, tomography always comes along the challenge of the proper acquisition of projection data where the measured intensity is monotonically related to a certain material property, e.g. mass-thickness. For certain applications, e.g. phase contrast nano-CT, the correct consideration of the imaging physics in 3D reconstruction algorithms remains a challenge. If not properly described, this can lead to strong reconstruction artefacts. Moreover, beam sensitivity or specific sample geometry may prevent the acquisition of full 180° tilt series with adequate angular sampling which would be required for artefact-free 3D reconstruction. A possible solution to reduce the amount of projection data required while maintaining reconstruction quality is to use compressed sensing approaches by taking into account certain prior knowledge about the sample characteristics, such as that the sample contains only a small number of piecewise constant material phases. In a first approach, we utilized this information by deriving valid constraints on the allowed reconstructions, whereas later, we first approximated the nonconvex Sobel operator to capture “sharp edges”, i.e., a rapid transition between material and void, and then nudge the compressed sensing algorithm towards reconstructing sharper edges.
Talare: Jan Glaubitz, MAI
Titel: Better together: Image reconstruction and Bayesian scientific computing
Sammanfattning: How can we recover clear, reliable images or signals when our observations are indirect, incomplete, and corrupted by noise? This challenge arises in many fields—from medical scans and satellite imaging to data analysis in science and engineering. Mathematically, such problems are known as inverse problems, and they are often “ill-posed,” meaning that small errors in the data can lead to large errors in the result. Traditional methods, such as compressive sensing, have shown impressive results in producing high-resolution reconstructions. However, these approaches can be sensitive to parameter choices and typically provide only a single “best guess” solution—without telling us how confident we should be in that result.
In this talk, I will describe how we can address these limitations by adopting a Bayesian perspective. Instead of producing just one answer, Bayesian methods treat image reconstruction as a problem of statistical inference: they combine information from the data (what we observed) with prior knowledge (what we expect the image to look like) to produce a full probability distribution of possible solutions. This distribution not only yields reconstructions that are robust but also provides a natural way to quantify uncertainty—for example, highlighting which parts of an image are reliable and which are not. I will discuss how we design priors that preserve essential features, such as edges, and how we efficiently compute with these models using ideas from optimization and measure transport. Additionally, I will explore how these methods perform in practice for applications in medical imaging, remote sensing, multi-measurement problems, and time-dependent imaging tasks.
Talare: Magnus Herberthson, MAI
Titel: Some optimization problems in diffusion MRI (magnetic resonance imaging)
Sammanfattningt: By performing a sufficient set of MRI measurement, it is possible to estimate various properties of tissue, e.g., the brain. Of interest for us is a second order tensor/matrix called the diffusion tensor and also a fourth order tensor (the covariance tensor). Finding these from the measurements is a fitting problem with can be solved by least squares. Under that approach, the estimates may be unphysical, and we discuss how one can use semidefinite programming to impose positivity conditions which are known to hold.
