Mathematical methods in biomedical imaging

摘要

Biomedical imaging is an important and exponentially growing field in life sciences and clinical practice, which strongly depends on the advances in mathematical image processing. Biomedical data presents a number of particularities such as non-standard acquisition techniques. Thus, biomedical imaging may be considered as an own field of research. Typical biomedical imaging tasks, as outlined in this paper, demand for innovative data models and efficient and robust approaches to produce solutions to challenging problems both in basic research as well as daily clinical routine. This paper discusses typical specifications and challenges of reconstruction and denoising, segmentation, and image registration of biomedical data. Furthermore, it provides an overview of current concepts to tackle the typically ill-posed problems and presents a unified framework that captures the different tasks mathematically.