Sparse Kaczmarz for Convergence Speed-Up in Multi-Contrast Magnetic Particle Imaging

Magnetic Particle Imaging (MPI) is a tracer-based medical imaging modality with great potential due to its high sensitivity, high spatio-temporal resolution, and capability to quantify the tracer distribution. Image reconstruction in MPI is an ill-posed problem, which regularization methods can address. In MPI, Tikhonov regularization is most commonly used and the corresponding optimization problem is usually solved using the Kaczmarz algorithm. Reconstruction using the Kaczmarz method for single-contrast MPI is very efficient as it produces the desired images fast after a small number of iterations. For multi-contrast MPI, however, the regular Kaczmarz algorithm fails to obtain good-quality images without channel leakage when using a small number of iterations. In this work, we propose a sparsity-promoting regularization term and an associated sparse Kaczmarz method in order to speed up convergence, especially in sparse channels. The proposed method reduces the channel leakage and as a result, speeds up convergence.