Purpose: Magnetic particle imaging (MPI) is a preclinical imaging technique capable of visualizing the spatio-temporal distribution of magnetic nanoparticles. The image reconstruction of this fast and dynamic process relies on efficiently solving an ill-posed inverse problem. Current approaches to reconstruct the tracer concentration from its measurements are either adapted to image characteristics of MPI but suffer from higher computational complexity and slower convergence or are fast but lack in the image quality of the reconstructed images. Methods: In this work we propose a novel MPI reconstruction method to combine the advantages of both approaches into a single algorithm. The underlying sparsity prior is based on an undecimated wavelet transform and is integrated into a fast row-action framework to solve the corresponding MPI minimization problem. Results: Its performance is numerically evaluated against a classical FISTA (Fast Iterative Shrinkage-Thresholding Algorithm) approach on simulated and real MPI data. The experimental results show that the proposed method increases image quality with significantly reduced computation times. Conclusions: In comparison to state-of-the-art MPI reconstruction methods, our approach shows better reconstruction results and at the same time accelerates the convergence rate of the underlying row-action algorithm.
