# Model-based inverse design

At the beginning of the imaging pipeline is the data acquisition, which measures the change of an emitted signal when interacting with sample.

This change can be measured physically on the one hand and modeled mathematically on the other. For a known sample, the response of the physical system can be determined from the model. Far more often, however, one would like to infer the nature of the sample from the measured response. To do this, the mathematical model must be inverted. These so-called inverse problems are at the heart of almost every imaging technique.

Our Model-Based Inverse Design Group builds on many years of experience at DESY in solving inverse problems, such as the phase problem in crystallography and coherent diffraction imaging, as well as the tomographic problem in many different variants. At our institute, applied mathematicians and computer scientists work together to analyze and solve inverse problems from a mathematical point of view. Our work includes learning-based algorithms for signal and image processing for phase field reconstruction, tomographic inversion as well as deconvolution and denoising. We have profound methodological knowledge on both the model level and the inverse design level and aim to pool expertise in inverse problems in a generic way to support other research groups dealing with image formation in the Helmholtz Association.

## Other Researches

### Image Analysis & Benchmarking

Helmholtz Imaging captures the world of science. Discover unique data sets, ready-to-use software tools, and top-level research papers.

The platform’s output originates from our research groups as well as from projects funded by us, theses supervised by us and collaborations initiated through us. Altogether, this showcases the whole diversity of Helmholtz Imaging.

### Projects

Helmholtz Imaging Projects are granted to cross-disciplinary research teams that identify innovative research topics at the intersection of imaging and information & data science, initiate cross-cutting research collaborations, and thus underpin the growth of the Helmholtz Imaging network. These annual calls are based on the general concept for Helmholtz Imaging and are in line with the future topics of the Initiative and Networking Fund (INF).

### Model-based inverse design

At the beginning of the imaging pipeline is the data acquisition, which measures the change of an emitted signal when interacting with sample. This change can be measured physically on the one hand and modeled mathematically on the other. For a known sample, the response of the physical system can be determined from the model. Far more often, however, one would like to infer the nature of the sample from the measured response. To do this, the mathematical model must be inverted. These so-called inverse problems are at the heart of almost every imaging technique.

### Integrative imaging data science

The amount of image data, algorithms and visualization solutions is growing vastly. This results in the urgent demand for integration across multiple modalities and scales in space and time. We develop and provide HIP solutions that can handle the very heterogeneous image data from the research areas of the Helmholtz Association without imposing restrictions on the respective image modalities. To lay the groundwork for the implementation of HIP solutions, our team at MDC will focus on the following research topics:

- Develop concepts and algorithms for handling and generic processing of high-dimensional datasets
- Develop algorithms for large, high-dimensional image data stitching, fusion and visualization