A Study on a Hybrid Reconstruction Algorithm for Three-Dimensional Magnetic Particle Imaging Based on Spatial Density Constraints and Residual Iterative Optimization

Magnetic particle imaging (MPI), as an emerging radiation-free, high-sensitivity molecular imaging technique, holds broad application prospects in fields such as medical diagnosis, angiography, and targeted drug tracking. However, traditional three-dimensional MPI reconstruction algorithms face a problem in balancing reconstruction speed and image resolution. A hybrid reconstruction algorithm (Full Hybrid) based on spatial density constraints and residual iterative optimization is proposed in this work. This paper simulates Lissajous trajectory scanning and the non-linear response of magnetic particles based on the three-dimensional MPI simulation framework. The proposed hybrid method first utilizes the X-space method to obtain a basic spatial prior, then introduces field-free point (FFP) trajectory density to impose spatial weighting constraints on the reconstructed image. Experimental results demonstrated that this hybrid algorithm performs better in the reconstruction of complex three-dimensional topological structures (an H-shaped phantom). Comprehensive evaluation demonstrated that the reconstructed outputs reach a peak signal-to-noise ratio (PSNR) of 12.85 dB, a structural similarity index measure (SSIM) of 0.7321, and a root mean square error (RMSE) of 0.2278. Ablation experiments and comparison experiments further reinforced the advantages of the proposed method. These results demonstrate the numerical feasibility of the proposed reconstruction method for a three-dimensional phantom and provide a basis for further evaluation under multiple simulation conditions and real-scanner measurements.