Dynamic image reconstruction in MPI with RESESOP-Kaczmarz

TL;DR

Dynamic MPI data suffer from motion artifacts when using stationary reconstruction methods. The paper introduces RESESOP-Kaczmarz, a dynamic inverse-solving framework that treats motion as forward-model inexactness and uses piecewise-constant concentration models $c(x,t)=c_{\tau_i}(x)$ over time subintervals, solving subproblems $A_i c_{\tau_i}=v_i$ with stripes and a discrepancy principle. Key contributions include data-driven estimation of inexactness levels $\zeta_i$, selection of efficient search directions to ensure convergence, and demonstration on simulated rotating-cylinder data and real capillary data, showing improved motion compensation over regularized Kaczmarz, with a trade-off between subframe size and noise. The approach enables subframe reconstruction in dynamic MPI with minimal priors, offering improved image quality for rapid particle movement and potential integration into existing MPI pipelines.

Abstract

In Magnetic Particle Imaging (MPI), it is typically assumed that the studied specimen is stationary during the data acquisition. In practical applications however, the searched-for 3D distribution of the magnetic nanoparticles might show a dynamic behavior, caused by e.g. breathing or movement of the blood. Neglecting those dynamics during the reconstruction step results in motion artifacts and a reduced image quality. This article addresses the challenge of capturing high quality images in the presence of motion. A promising technique provides the Regularized Sequential Subspace Optimization (RESESOP) algorithm, which takes dynamics as model inexactness into account, significantly improving reconstruction compared to standard static algorithms like regularized Kaczmarz. Notably, this algorithm operates with minimal prior information and the method allows for subframe reconstruction, making it suitable for scenarios with rapid particle movement. The performance of the proposed method is demonstrated on both simulated and real data sets.

Figures (6)

• Figure 1: Reconstruction results with regularized Kaczmarz from noise free data of a fast rotating cylinder.
• Figure 2: Illustration of a stripe
• Figure 3: The course of the motion illustrated by the ground truth phantom at the beginning of each trajectory of the fast rotation (seven fpr).
• Figure 4: Dynamic Reconstructions of frame four from noisy simulated data with two different rotation speeds. The left column shows results for a rotation speed of 44 fpr, the right column for seven fpr.
• Figure 5: Mean squared error in dependence on the amount of RESESOP-Kaczmarz loops.