Applications of PDEs inpainting to magnetic particle imaging and corneal topography

Opuscula Mathematica

article

Andrea Andrisani¹  Rosa Maria Mininni¹  Francesca Mazzia²  Giuseppina Settanni¹  Alessandro Iurino³  Sabina Tangaro⁴  Andrea Tateo³  Roberto Bellotti⁴ 

[1] Università degli Studi di Bari Aldo Moro, Dipartimento di Matematica;Università degli Studi di Bari Aldo Moro, Dipartimento di Informatica;Università degli Studi di Bari Aldo Moro, Dipartimento Interateneo di Fisica "M. Merlin";Istituto Nazionale di Fisica Nucleare

关键词: PDEs inpainting;    medical imaging;    magnetic particle imaging;    radial curvature image;    anterior surface of a cornea.;   

DOI  :  10.7494/OpMath.2019.39.4.453

学科分类：环境科学（综合）

来源: AGH University of Science and Technology Press

【 摘 要 】

In this work we propose a novel application of Partial Differential Equations (PDEs) inpainting techniques to two medical contexts. The first one concerning recovering of concentration maps for superparamagnetic nanoparticles, used as tracers in the framework of Magnetic Particle Imaging. The analysis is carried out by two set of simulations, with and without adding a source of noise, to show that the inpainted images preserve the main properties of the original ones. The second medical application is related to recovering data of corneal elevation maps in ophthalmology. A new procedure consisting in applying the PDEs inpainting techniques to the radial curvature image is proposed. The images of the anterior corneal surface are properly recovered to obtain an approximation error of the required precision. We compare inpainting methods based on second, third and fourth-order PDEs with standard approximation and interpolation techniques.

【 授权许可】

CC BY-NC