Simultaneous relaxation estimation and image reconstruction in MPI

Blurring of the images due to the relaxation effects of the magnetic nanoparticles is one of the important issues in Magnetic Particle Imaging (MPI)^[1-4]. In x-space reconstructed images, relaxation blurs the image along the scanning direction, and deteriorates both the resolution and the signal-to-noise ratio (SNR) of the image^[5]. Hence, removing the effects of relaxation without distorting the underlying image is crucial for increasing the efficiency of the MPI technique. Theoretically, relaxation is modelled as an exponential function r(t) = (1/τ)exp(-t/τ)u(t) using the first-order Debye process, where r(t) is then convolved with the adiabatic MPI signal^[5]. Previous studies have looked into estimating the relaxation time constant, τ, using a calibration scan on a point source or using an MPI relaxometer setup^[5]. In theory, if one can estimate the relaxation time constant, a deconvolution technique could be employed to obtain the underlying adiabatic MPI signal, which would yield an image unaffected by the relaxation blur. In this work, we propose a solution for blind estimation of τ directly from the MPI signal, without using a calibration scan and without the knowledge of the Langevin response of the nanoparticles.