ABBA

AB-GMRES and BA-GMRES as Regularizing Iterations for X-Ray CT

The material on this homepage is related to the AB-GMRES and BA-GMRES iterative Krylov subspace methods (jointly referred to as ABBA methods). These methods are suited for computing reconstructions with an unmatched pair of forward and back projects, which is often the case in X-ray CT. The methods are described here:

P. C. Hansen, K. Hayami, and K. Morikuni, GMRES methods for tomogarphic reconstruction with an unmatched back projector, J. Comp. Appl. Math., 413 (2022), 114352; DOI 10.1016/j.cam.2022.114352 open access. This work was supported by grant no. S19008 from Japan Society for the Promotion of Science.
The talk GMRES-Based Methods for Unmatched Projectors in X-Ray CT given at SIAM IS24.

We provide three Matlab functions that can be downloaded individually:

ABgmres implementation of the AB-GMRES algorithm.
BAgmres implementation of the BA-GMRES algorithm.
NCPforCT implementation of the NCP method for CT problems.

We also provide Python software that implements the ABBA methods:

Master Thesis ABBA Iterative methods for X-Ray Computed Tomography by Maria Knudsen, supervised by Per Christian Hansen and Research Professor Emil Y. Sidky, University of Chicago.
GitHub page with the Python software.

Moreover, we provide Matlab code (also written by Maria Knudsen) that uses the ASTRA Toolbox to produce the forward and back projector pairs in the form of objects/operators or sparse matrices. The CPU version of ASTRA produces matched matched pairs; the GPU version produces unmatched pairs:

GitHub page with the Matlab software, installation instructions, and information about which discretization models are available.

We know that not everyone may have access to ASTRA and a GPU, and hence we provide a few test problems as MATLAB mat-files in this REPOSITORY.

Python implementations are also available in TIGRE: Tomographic Iterative GPU-Based Reconstruction Toolbox.

Please report bugs to Per Christian Hansen pcha@dtu.dk.