We propose to initiate a new research direction on the mathematics of dynamic 3D imaging problems, within the CWI Computational Imaging group. While classical 3D scanning techniques (CT, MRI, ultrasound, etc.) are mainly designed for scanning static objects, there is a growing interest in capturing the 4D (3D space + time) evolution of dynamic processes. Mathematics forms the key to making this possible. The fundamental scientific challenge of dynamic 3D imaging is the lack of sufficient image data in each individual time frame, making it impossible to solve the 3D inverse problem separately for each point in time. Instead, we need to link the 3D images by a dynamical system model of the object’s evolution, creating a complex new type of inverse problem that involves estimating both the 4D image data and the parameters governing the dynamical system simultaneously. Current mathematical and computational techniques are insufficient for dealing with these challenging problems. The proposed Tenure Track position is situated at the interface of the NDNS+ and DIAMANT clusters: - Dynamical systems theory, modeling, and simulation form the scientific context for describing the evolution of the scanned object. - Discrete inversion techniques and convex optimization methods form the scientific context for solving the inverse problems relating the measurement to the scanned object. We envision that the appointed Tenure Track candidate will play a key role in establishing cross-domain relationships between these clusters, while at the same time performing research in an important emerging field.