A fused LASSO operator for fast 3D magnetic particle imaging reconstruction

Abstract Objective. Magnetic particle imaging (MPI) is a promising imaging modality that leverages the nonlinear magnetization behavior of superparamagnetic iron oxide nanoparticles to determine their concentration distribution. Previous optimization models with multiple regularization terms have been proposed to achieve high-quality MPI reconstruction, but these models often result in increased computational burden, particularly for dense gridding 3D fields of view. In order to achieve faster reconstruction speeds without compromising reconstruction quality, we have developed a novel fused LASSO operator, total sum-difference (TSD), which effectively captures the sparse and smooth priors of MPI images. Methods. Through an analysis-synthesis equivalence strategy and a constraint smoothing strategy, the TSD regularized model was solved using the fast iterative soft-thresholding algorithm (FISTA). The resulting reconstruction method, TSD-FISTA, boasts low computational complexity and quadratic convergence rate over iterations. Results. Experimental results demonstrated that TSD-FISTA required only 10% and 37% of the time to achieve comparable or superior reconstruction quality compared to commonly used fused LASSO-based alternating direction method of multipliers and Tikhonov-based algebraic reconstruction techniques, respectively. Significance. TSD-FISTA shows promise for enabling real-time 3D MPI reconstruction at high frame rates for large fields of view.