Signals and Systems in Englisch

- Signal processing (recapitulation of fundamental principles in signal processing) - Mathematical methods in image reconstruction and signal processing - X-Ray (fundamental principles, quantum statistics) - Computed Tomography

- devices, - current and past technology, - signal processing, - Fourier-based 2D and 3D image reconstruction, - algebraic and statistical image reconstruction, - image artifacs, - technical and clinical applications, - dose.

This lecture gives a comprehensive overview of the main signal processing and system analysis methods in medical imaging. The basis of the reconstruction is undoubtedly mathematics. However, the beauty of e.g. computed tomography cannot be understood without a basic knowledge of X-ray physics, signal processing concepts and measurement systems. Therefore, students will be provided with a number of references to these basic disciplines as well as a brief introduction to many of the underlying principles. The main application focus of the lecture is given to computed tomography. The lecture is structured to cover the basics of signals and systems within CT, from photon statistics to modern cone-beam systems. However, without an elementary knowledge of X-ray physics, a number of the described imaging effects and artifacts cannot readily be understood. In the main part of the lecture the principles of signal processing are reviewed. This part focuses on the necessary background of computed tomography and, consequently, introducing the Fourier transform. Subsequently, a detailed overview of two-dimensional reconstruction mathematics is given as a straight forward application of the Fourier principles. Then, algebraic and statistical approaches are explained as a general tool for signal analysis and over-determined system solution. In the last lessons three-dimensional methods of CT image or volume reconstruction are reviewed. It is shown that some of the ideas are consequent extensions of the methods discussed the beginning of the lecture. The methods described here represent the basis of a highly active field of research.

- Computed Tomography, From Photon Statistics to Modern Cone Beam CT, T. M. Buzug, Springer-Verlag, Berlin/Heidelberg, 2008. - Einführung in die Computertomographie, Mathematisch-physikalische Grundlagen der Bildrekonstruktion, T. M. Buzug, Springer-Verlag, Berlin/Heidelberg, 2004.

- Fundamental principles in mathematics and signal processing (signal transmission, Fourier transform, sampling theorem, ...) - Basic knowledge about medical imaging