A Fourier slice theorem for magnetic particle imaging using a field-free line

The magnetic particle imaging method is capable of imaging the distribution of magnetic nanoparticles in vivo. The sensitivity of the method can be significantly improved using a signal encoding scheme, which applies a field-free line (FFL) instead of the commonly used field-free point (FFP). Recent efforts have considerably improved the efficiency of the coil topology used to generate the FFL. However, until now it has not been investigated how the reconstruction of the particle distribution can be efficiently carried out when using the FFL encoding scheme. In this work, it is shown that the induced signal is linked to the Radon transform of the particle distribution. Hence, a fast algorithm for the reconstruction of the particle distribution can be derived, which first transforms the induced signal into Radon space and second applies a common reconstruction algorithm to transform the Radon data into image space.