A Strategy for the Extension of the Kaczmarz Algorithm to Different Priors

This work introduces a strategy for the extension of the standard weighted Kaczmarz algorithm, which is commonly used with Tikhonov regularization in system-matrix based magnetic particle imaging, to other priors. The proposed reformulation of the algorithm allows us to include more sophisticated priors while inheriting the fast convergence of the Kaczmarz iteration. The new method is developed with help of the alternating direction method of multipliers. The results show that also with a suboptimal alternating direction method of multiplier steps, the proposed algorithm solves the problem with very high convergence rate.