Spike localization in Zero Time of Echo (ZTE) magnetic resonance imaging

This paper considers Magnetic Resonance Imaging (MRI) of objects which are assumed to be composed of only a finite number of spikes. These spikes could be the population of cells labeled with perfluorocarbon nanoemulsion tracer agents for 19F MRI detection, used for cell tracking applications. It is further assumed that samples in the k-space are acquired through a 3D radial sampling scheme. This scenario can happen when one is using a Zero Time of Echo (ZTE) sampling technique, in which the data acquisition is started immediately after radiofrequency (RF) excitation pulse. Due to the structure of 3D radial sampling, one may not be able to use conventional 3D Fourier transform in order to reconstruct the image, as the samples are not located on Cartesian grid. We directly write the Fourier transform in the spherical domain, and by computing Spherical Harmonic Transforms (SHT) along concentric spheres, we cast this problem as decomposition of spherical Bessel functions. By using an approximation of spherical Bessel function, we rewrite this problem as a variant of atomic norm minimization framework, which could be written as a convex semidefinite program (SDP), and can be solved by off-the-shelf solvers. Our approach shows a promising numerical performance. 1