Image reconstruction techniques in muography: A review of algorithms and physical principles

Muography utilizes the interaction characteristics of high-energy cosmic-ray muons with matter to enable non-destructive inspection and internal imaging of large-scale or shielded objects. This review focuses on the fundamental interaction mechanisms between muons and matter and introduces three major categories of muography: muon scattering imaging, muon transmission imaging, and muon and muonic secondary particle imaging. For each technique, representative reconstruction algorithms are described, implemented, and comparatively analyzed. In muon scatter imaging, the point-of-closest-approach method is discussed alongside enhancements using the statistical modeling and clustering techniques to improve accuracy in complex environments. For muon transmission imaging, the limitations of the classical flux ratio method are examined, and alternative approaches, such as the density inversion algorithm and the inverse reconstruction algorithm, based on the medical imaging method are evaluated for reconstructing large-scale density distributions. For muon and muonic secondary particle imaging technology, coinciding muon trajectory density tomography is studied. Furthermore, a multi-modal imaging approach is proposed that combines scattering and coinciding muon trajectory density tomography. The study also explores coinciding muon trajectory density tomography based on artificial muon sources to expand the application boundaries of muography. By synthesizing representative algorithms and evaluating their performance across different application scenarios, this paper serves both as a comprehensive overview and a practical guideline for researchers and engineers. It aims to support the implementation and selection of suitable muography algorithms in fields, such as nuclear security, geological exploration, and industrial non-destructive testing.