Research of magnetic particle imaging reconstruction based on the elastic net regularization

Accurate Concentration Recovery for Quantitative Magnetic Particle Imaging Reconstruction via Nonconvex Regularization

Magnetic particle imaging (MPI) uses nonlinear response signals to noninvasively detect magnetic nanoparticles in space, and its quantitative properties hold promise for future precise quantitative treatments. In reconstruction, the system matrix based method necessitates suitable regularization terms, such as Tikhonov or non-negative fused lasso (NFL) regularization, to stabilize the solution. While NFL regularization offers clearer edge information than Tikhonov regularization, it carries a biased estimate of the l1 penalty, leading to an underestimation of the reconstructed concentration and adversely affecting the quantitative properties. In this paper, a new nonconvex regularization method including min-max concave (MC) and total variation (TV) regularization is proposed. This method utilized MC penalty to provide nearly unbiased sparse constraints and adds the TV penalty to provide a uniform intensity distribution of images. By combining the alternating direction multiplication method (ADMM) and the two-step parameter selection method, a more accurate quantitative MPI reconstruction was realized. The performance of the proposed method was verified on the simulation data, the Open-MPI dataset, and measured data from a homemade MPI scanner. The results indicate that the proposed method achieves better image quality while maintaining the quantitative properties, thus overcoming the drawback of intensity underestimation by the NFL method while providing edge information. In particular, for the measured data, the proposed method reduced the relative error in the intensity of the reconstruction results from 28% to 8%.

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

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.