A Blind Deconvolution Technique Based on Projection Onto Convex Sets for Magnetic Particle Imaging

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.