  Magnetic Particle Imaging (MPI) is an emerging imaging modality that maps the
spatial distribution of magnetic nanoparticles. The x-space reconstruction in
MPI results in highly blurry images, where the resolution depends on both
system parameters and nanoparticle type. Previous techniques to counteract this
blurring rely on the knowledge of the imaging point spread function (PSF),
which may not be available or may require additional measurements. This work
proposes a blind deconvolution algorithm for MPI to recover the precise spatial
distribution of nanoparticles. The proposed algorithm exploits the observation
that the imaging PSF in MPI has zero phase in Fourier domain. Thus, even though
the reconstructed images are highly blurred, phase remains unaltered. We
leverage this powerful property to iteratively enforce consistency of phase and
bounded l1 energy information, using an orthogonal Projections Onto Convex Sets
(POCS) algorithm. To demonstrate the method, comprehensive simulations were
performed without and with nanoparticle relaxation effects, and at various
noise levels. In addition, imaging experiments were performed on an in-house
MPI scanner using a three-vial phantom that contained different nanoparticle
types. Image quality was compared with conventional deconvolution methods,
Wiener deconvolution and Lucy-Richardson method, which explicitly rely on the
knowledge of PSF. Both the simulation results and experimental imaging results
show that the proposed blind deconvolution algorithm outperforms the
conventional deconvolution methods. Without utilizing the imaging PSF, the
proposed algorithm improves image quality and resolution even in the case of
different nanoparticle types, while displaying reliable performance against
loss of the fundamental harmonic, nanoparticle relaxation effects, and noise.
