Extension of the Kaczmarz algorithm with a deep plug-and-play regularizer

The Kaczmarz algorithm is widely used for image reconstruction in magnetic particle imaging (MPI) because it converges rapidly and provides good image quality even after a few iterations. It is often combined with Tikhonov regularization to cope with noisy measurements and the ill-posed nature of the imaging problem. In this abstract, we propose to combine the Kaczmarz method with a plug-and-play (PnP) denoiser for regularization, which can provide more specific prior knowledge than handcrafted priors. Using measurement data of a spiral phantom, we show that Kaczmarz-PnP yields excellent image quality, while speeding up the already fast convergence. Since the PnP denoiser is not coupled to the imaging operator, the Kaczmarz-PnP method is very generic and can be used for image reconstruction independently of the measurement sequence and MPI tracer type.