Multi-harmonic gridded 3D deconvolution (MH3D) for robust and accurate image reconstruction in MPI for single axis drive field scanners

<i>Objective</i>. This work introduces a new magnetic particle imaging (MPI) reconstruction framework based on multi-harmonic 3D deconvolution (MH3D) of gridded portraits, offering a principled, model-driven approach to MPI imaging.<i>Approach</i>. MH3D defines a convolutional forward model using higher harmonic portraits, which are gridded images formed from filtered frequency-domain signal components. Each harmonic portrait is modeled as a convolution with a distinct PSF, closely approximated by derivatives of the Langevin function, and incorporates receive sensitivity and mesh downsampling for accurate modeling. We also introduce practical strategies for calibration, phase correction, and artifact reduction.<i>Main Results</i>. We validate the MH3D approach using analytic approximations, numerical simulations, and experimental phantom data. MH3D yields high-resolution 3D reconstructions on seconds-scale runtimes, improves image quality relative to common 3rd-harmonic-only reconstructions, and achieves image quality and resolution comparable to a generalized model-based method in simulations and phantom experiments.<i>Significance</i>. This work offers new theoretical insight into MPI signal structure, unveiling the methodological and theoretical underpinnings absent in earlier single-harmonic or heuristic methods, thereby supporting accurate and robust 3D imaging with excellent computational efficiency.