Dynamic residual Kaczmarz method for noise reducing reconstruction in magnetic particle imaging

Abstract

Objective. Here, we propose a dynamic residual Kaczmarz (DRK) method as an improved reconstruction method for magnetic particle imaging (MPI) to achieve a better reconstruction quality from high-noise signals. Approach. Based on the Kaczmarz (KZ) method, we introduced a residual vector to select parts of the low-noise equations for reconstruction. In each iteration, a low-noise subset was formulated based on the residual vector. Thus, the reconstruction converged to an accurate result with less noise. Main Results. To evaluate the performance of the proposed method, it was compared with classical Kaczmarz-type methods and state-of-the-art regularization models. The numerical simulation results demonstrate that the DRK method can achieve better reconstruction quality than all other comparison methods at similar noise levels. It can acquire a signal-to-background ratio (SBR) that is five times higher than that of classical Kaczmarz-type methods at a 5 dB noise level. Furthermore, the DRK method can acquire up to 0.7 structural similarity (SSIM) indicators at a 5 dB noise level when combined with the non-negative fused Least absolute shrinkage and selection operator (LASSO) regularization model. In addition, a real experiment based on the OpenMPI data set validated that the proposed DRK method can be applied to real data and perform well. Significance. The experimental results demonstrate that the proposed DRK method can significantly improve the reconstruction quality of MPI when the signals contain high noise. It has the potential to be applied to MPI instruments that contain high signal noise, such as human-sized MPI instruments. It is beneficial for expanding the biomedical applications of MPI technology.