ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing

We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H−1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation

The development of an obstetric tele-monitoring system

Fetal growth restriction and preterm uterine contractions can turn a normal pregnancy into a problematic one. In previous work, we have developed a system for electrophysiological measurement of fetal heart rate (fHR), fetal electrocardiogram (fECG) and (premature) uterine contractions to enable early detection of foetal problems. In this work we have expanded this system into a tele-monitoring system for measurement at home. In order to permit home monitoring, the communication chain of the data has to be designed such that home-measured signals (fHR, fECG, uterine activities) are available in the hospital in real-time. Furthermore, the data must be transferred wirelessly to any location (worldwide) for interpretation by gynaecologists. A web application helps the gynaecologist or midwife to access the signals everywhere, provided that internet access is available. We developed a webserver as the heart of the entire system; it manages the patient database, transforms the signals in a graphical representation similar to that of the cardiotocography and manages the data communication with the proper data security policy. This tele-monitoring system can be used also during home deliveries enabling prompt transfer and proper intervention in the hospital when complications occu