Multi-harmonic Gridded 3D Deconvolution (MH3D) for Image Reconstruction in MPI: MH3D

Abstract

We have developed a new effective methodology called multi-harmonic gridded 3D deconvolution (MH3D) for image reconstruction in magnetic particle imaging (MPI). This new methodology in turn has led to important new theoretical insights into this complex problem. The technique works by first mapping the MPI harmonics into the spatial domain by gridding the time domain data to their respective field free regions (FFRs).  We refer to these spatially gridded harmonic data as harmonic portraits since they represent only a portrait-like representation of the true image. The final true image is then formed by inverting these harmonic portraits, which is effectively accomplished via a 3D deconvolution with harmonic point spread functions (PSFs). The PSFs are the harmonic portrait signatures resulting from a scanned point source. They are formed through a simulated MPI system model of the scanner and magnetic tracers, while additional results indicate that they can be modeled analytically. Additional MPI scanner parameters can be modeled into MH3D, such as multiple and non-uniform receive coils.

Analytical and numerical results indicate that our method is lossless, in the sense that it retains all the information coming from an MPI signal. The primary computational advantage of our approach is the ability to easily perform artifact analysis and correction techniques made available to us in the intermediate harmonic portrait domain, which has greatly aided in the hardware development of a clinical scale system. Our new approach also provides new key theoretical insights into the MPI reconstruction problem. Namely, we have shown that it is possible to faithfully reconstruct images using only the second harmonic, albeit at the cost of lower spatial resolution. Alternatively, high resolution imaging is possible with only the second harmonic provided sufficiently dense FFR scanning patterns.  This also suggested that a narrow band receive chain could be implemented in the hardware. However, higher harmonics become increasingly important at higher drive field amplitudes.