Medical imaging: state of the art and future development

An overview on medical imaging techniques is given from an algorithmic point of view. The mathematical framework, inverse problems and regularization, is sketched. The radon transform serves as mathematical model for studying resolution, noise amplification and inversion methods in reconstruction problems. The imaging techniques discussed are X-ray computer tomography, magnetic resonance imaging, ultrasound tomography, impedance computer tomography, diffuse tomography, biomagnetism and emission computer tomography as single-particle emission tomography and positron emission tomography. There are close connections to nondestructive evaluation.