  The aim of magnetorelaxometry imaging is to determine the distribution of
magnetic nanoparticles inside a subject by measuring the relaxation of the
superposition magnetic field generated by the nanoparticles after they have
first been aligned using an external activation magnetic field that has
subsequently been switched off. This work applies techniques of Bayesian
optimal experimental design to (sequentially) selecting the positions for the
activation coil in order to increase the value of data and enable more accurate
reconstructions in a simplified measurement setup. Both Gaussian and total
variation prior models are considered for the distribution of the
nanoparticles. The former allows simultaneous offline computation of optimized
designs for multiple consecutive activations, while the latter introduces
adaptability into the algorithm by using previously measured data in choosing
the position of the next activation. The total variation prior has a desirable
edge-enhancing characteristic, but with the downside that the computationally
attractive Gaussian form of the posterior density is lost. To overcome this
challenge, the lagged diffusivity iteration is used to provide an approximate
Gaussian posterior model and allow the use of the standard Bayesian A- and
D-optimality criteria for the total variation prior as well. Two-dimensional
numerical experiments are performed on a few sample targets, with the
conclusion that the optimized activation positions lead, in general, to better
reconstructions than symmetric reference setups when the target distribution or
region of interest are nonsymmetric in shape.
