Inverse Problems with sparse data: a challenge in the exploration of Earth and space

Sparse or insufficient data is often our only direct source of information when 
studying distant or hidden objects. Notable examples of this can be found in 
the exploration of planetary interiors, the Sun's interior, or distant 
planetary systems. At a first glance it seem that sparse data inevitably leads 
to poor models, but methods exist that allow us to improve the quality of the 
data analysis. We shall see how data can be successfully supplemented with 
external physical information to obtain consistent solutions, and we will 
discuss how the influence of observational noise can be kept under control.