Dynamic Bayesian models and model approximation in inverse problems with applications

Inverse problems arise in many fields of applied science, for example in medicine, engineering and data science. They deal with deducing cause from effect. In image processing for example, sharpening a blurry image can be seen as an inverse problem. This thesis highlights some of the key difficulties in solving inverse problems. Statistical formulation of the problem is given and different solution methods are introduced. The methods are then used in real-world applications in genetics, ultrasound imaging and signal processing.