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Updated: Jul 30, 2025

Digital Hybrid Model Preparation for Virtual Planning of Reconstructive Dentoalveolar Surgical Procedures

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On Krylov methods for large-scale CBCT reconstruction.

Malena Sabaté Landman¹, Ander Biguri¹, Sepideh Hatamikia^2,3

¹Department of Applied Mathematics and Theoretical Physics (DAMTP), University of Cambridge, Cambridge, United Kingdom.

Physics in Medicine and Biology

|May 16, 2023

Summary

This summary is machine-generated.

Krylov subspace methods offer efficient, regularized solutions for large-scale computed tomography (CT) inverse problems. This work introduces an open-source framework to enhance their application in medical physics and engineering.

Keywords:

CBCT CT Krylov methods inverse problems iterative reconstruction open source total variation

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Area of Science:

Numerical linear algebra
Applied medical physics
Computational imaging

Background:

Krylov subspace methods are efficient iterative solvers for linear systems.
They possess intrinsic regularization properties suitable for inverse problems.
Their application in large-scale medical imaging, like computed tomography (CT), remains limited.

Purpose of the Study:

To bridge the gap in applying Krylov subspace methods to 3D CT reconstruction.
To provide a general framework for relevant Krylov solvers in CT.
To promote accessibility and reproducibility through an open-source toolbox.

Main Methods:

Implementation of Krylov solvers (CGLS, LSQR, LSMR) for non-square systems.
Integration with Tikhonov and total variation regularization.
Development within an open-source, GPU-accelerated framework.

Main Results:

Numerical comparisons of Krylov methods on synthetic and real-world 3D CT data.
Demonstration of suitability for various CT applications (CBCT, μ-CT).
Validation of the open-source toolbox for reproducible research.

Conclusions:

Krylov subspace methods are highly suitable for large-scale 3D CT reconstruction.
The open-source framework facilitates their adoption in medical physics and engineering.
The study provides a valuable resource for researchers and practitioners in CT imaging.