Fast MPI reconstruction with non-smooth priors by stochastic optimization and data-driven splitting.

Area of Science:

• Medical Imaging
• Computational Science
• Applied Mathematics

Background:

• Magnetic particle imaging (MPI) reconstruction commonly uses Tikhonov regularization (l2) with the Kaczmarz method.
• Advanced regularization techniques like l1 or TV regularization improve image quality but are incompatible with standard Kaczmarz methods.

Purpose of the Study:

• To develop a flexible and efficient reconstruction algorithm for magnetic particle imaging.
• To enable the use of advanced regularization techniques for improved image quality.
• To achieve reconstruction speeds comparable to or exceeding current state-of-the-art methods.

Main Methods:

• Implementation of a stochastic primal-dual hybrid gradient (SPDHG) method.
• Integration of various data fitting terms and regularization strategies within the SPDHG framework.
• Development of novel step size rules and a data-driven splitting scheme for accelerated convergence.

Main Results:

• The proposed SPDHG algorithm demonstrates comparable run times to existing methods.
• Significant improvements in reconstruction quality are achieved through flexible integration of regularization terms.
• New step size rules and splitting schemes lead to faster convergence and easier algorithm handling.

Conclusions:

• The SPDHG method offers enhanced flexibility and improved image quality for magnetic particle imaging reconstruction.
• The developed acceleration techniques make the algorithm highly efficient and user-friendly.
• This approach advances MPI reconstruction capabilities by overcoming limitations of classical methods.