Many important real world problems give rise to an Inverse problem (IP). These include medical imaging, non-destructive testing, oil and gas exploration, land-mine detection and process control. For example, in the exploration for oil and gas, one needs to assess the structure of the interior of the earth from observations made at the surface. Typically, an explosion is created and the resulting shockwaves together with their reflections are used to build a model of the structure of the earth. In magnetoencephalography one needs to determine the electric current in the neurones from the...