Tomography: mathematical aspects and applications

2015/01/29 by Paolo Facchi, Marilena Ligabò, Sergio Solimini · 5 citations
Mathematics · Medicine · Physics and Astronomy · #Advanced Harmonic Analysis Research #Interpretation (philosophy) #Medical Imaging Techniques and Applications #Minification #Numerical methods in inverse problems #Radon #Radon transform #Tomographic reconstruction #Tomography #math-ph #math.MP

paper · pdf · doi:10.1088/0031-8949/90/7/074007

published in Physica Scripta 90(7), 074007 (IOP Publishing) · 11 pages, 5 figures

arxiv created 2015/01/29 · openalex publication_date 2015/06/01 · arxiv updated 2015/06/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

In this article we present a review of the Radon transform and the instability of the tomographic reconstruction process. We show some new mathematical results in tomography obtained by a variational formulation of the reconstruction problem based on the minimization of a Mumford–Shah type functional. Finally, we exhibit a physical interpretation of this new technique and discuss some possible generalizations.

Citations

• Classical and quantum aspects of tomography
• Distribution functions in physics: Fundamentals
• Determination of quasiprobability distributions in terms of probability distributions for the rotated quadrature phase
• On the inversion of the Radon transform: standard versus M 2 approach
• Optimal approximations by piecewise smooth functions and associated variational problems
• Quantum mechanics as a statistical theory
• On the Quantum Correction For Thermodynamic Equilibrium