AbstractMagnetorelaxometry imaging is a highly sensitive technique enabling noninvasive, quantitative detection of magnetic nanoparticles. Electromagnetic coils are sequentially energized, aligning the nanoparticles’ magnetic moments. Relaxation signals are recorded after turning off the coils. The forward model describing this measurement process is reformulated into a severely ill-posed inverse problem that is solved for estimating the particle distribution. Typically, many activation sequences employing different magnetic fields are required to obtain reasonable imaging quality. We seek to improve the imaging quality and accelerate the imaging process using fewer activation sequences by optimizing the applied magnetic fields. Minimizing the Frobenius condition number of the system matrix, we stabilize the inverse problem solution toward model uncertainties and measurement noise. Furthermore, our sensitivity-weighted reconstruction algorithms improve imaging quality in lowly sensitive areas. The optimization approach is employed to real measurement data and yields improved reconstructions with fewer activation sequences compared to non-optimized measurements.
Convexification for a 1D hyperbolic coefficient inverse problem with single measurement data
