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

Magnetic particle imaging (MPI) maps the spatial distribution of superparamagnetic iron oxide nanoparticles (SPIO) by leveraging the particles’ nonlinear magnetization response. In x-space image reconstruction, MPI images are spatially blurred as a result of the nature of this response, as well as nanoparticle relaxation effects. In this article, we present a deconvolution method for MPI based on convex sets constructed from the phase of the Fourier Transform and bounded `1 energy of a given image. The proposed method relies on the observation that imaging point spread functions (PSF) in MPI have zero phase in Fourier domain. Thus, although images are blurred, phase information is unaltered in Fourier domain. The proposed deconvolution method iteratively enforces consistency of phase and other spatial information using an orthogonal Projections Onto Convex Sets (POCS) algorithm. Comparisons are performed against Wiener and Lucy-Richardson deconvolution methods. The proposed method outperforms conventional methods in terms of image quality, and it demonstrates reliable performance against loss of the fundamental harmonic, nanoparticle relaxation effects, and noise.