Learning Regularization Parameter-Maps for Variational Image Reconstruction using Deep Neural Networks and Algorithm Unrolling

Andreas Kofler (PTB) published together with Fabian Altekrüger (TU Berlin), Fatima Antarou Ba (TU Berlin), Christoph Kolbitsch(PTB), Evangelos Papoutsellis (Finden Ltd), David Schote (PTB), Clemens Sirotenko (WIAS), Felix Frederik Zimmermann (PTB) and Kostas Papafitsoros (QMUL) an article in SIAM Imaging Sciences.

The article describes a new method for learning regularization parameter-maps which can be used for variational image reconstruction. The proposed approach involves an end-to-end trainable network which consists of two distinct sub-networks: the first which estimates regularization parameter-maps and the second which reconstructs images using the primal dual hybrid gradient algorithm.

In the article the method is applied to total variation-minimization based reconstruction for different imaging problems: dynamic cardiac MRI, T1-mapping in the brain, dynamic image denoising and low-dose computed tomography.

The obtained regularization parameter-maps further enhance the quality of the TV-reconstructions which can be obtained by only using scalar regularization parameters and naturally adapt to the data used for training.

This project was initiated by the Hackathon "Math Meets Image" organised by Felix Ambellan (ZIB), Robert Beinert (TU Berlin), Christoph Kolbitsch (PTB), Kostas Papafitsoros (WIAS) and Christoph von Tycowicz (FU Berlin, ZIB) as part of the Math+ Thematic Einstein Semester on "Mathematics of Imaging in real-world challenges". It brought together young scientists from a wide range of Berlin institutions to solve a challenging problem with application in different medical imaging fields such as MRI and CT but also for processing of video sequences.

A preprint of the accepted article is available at https://arxiv.org/abs/2301.05888. An implementation of the code will be made available at https://github.com/koflera/LearningRegularizationParameterMaps.

Contact:

Andreas Kofler, E-Mail: 📧 andreas.kofler(at)ptb.de