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.

翻译：磁松弛成像的目标是通过测量磁性纳米粒子在经外部激活磁场对齐（随后关闭）后产生的叠加磁场弛豫信号，来确定受试对象体内磁性纳米粒子的分布。本研究应用贝叶斯最优实验设计技术（顺序）选择激活线圈位置，以提升数据价值并在简化测量设置下实现更精确的重建。针对纳米粒子分布，分别采用高斯先验模型与全变差先验模型。前者允许对多次连续激活的优化设计进行离线同步计算，而后者通过利用先前测量数据选择下一次激活位置引入算法自适应性。全变差先验具有理想的边缘增强特性，但其缺陷在于失去了计算上极具吸引力的高斯后验密度形式。为克服这一挑战，采用滞后扩散迭代法构建近似高斯后验模型，从而也使得全变差先验能够适用标准贝叶斯A-最优与D-最优准则。基于若干样本目标的二维数值实验表明：当目标分布或感兴趣区域形状非对称时，优化激活位置通常能比对称参考设置获得更好的重建效果。