Before revision:  We test our framework using various parameterisations including one that combines a truncated Whittle-Matern (WM) level-set function with other WM fields to characterise spatial variability of the physical property on each region. We use these parameterisations to solve PDE-constrained identification problems arising in (i) medical imaging where the aim is to detect the existence and properties of diseased tissue and (ii) non-destructive testing (NDT) of materials from data collected during manufacturing processes. We provide comparisons against a standard method  and demonstrate that the proposed method is  viable choice to address computational efficiency of EKI in practical/operational settings.
After revision:  We compare the proposed technique with a standard method and demonstrate that the proposed method is viable choice to address computational efficiency of EKI in practical/operational settings.