TY  - JOUR
ID  - Andrisani2019
LB  - Andrisani2019
AU  - Andrisani, Andrea
AU  - Mininni, Rosa Maria
AU  - Mazzia, Francesca
AU  - Settanni, Giuseppina
AU  - Iurino, Alessandro
AU  - Tangaro, Sabina
AU  - Tateo, Andrea
AU  - Bellotti, Roberto
TI  - Applications of PDEs inpainting to magnetic particle imaging and corneal topography
ST  - Applications of PDEs inpainting to magnetic particle imaging and corneal topography
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2019
VL  - 39
IS  - 4
SP  - 453
EP  - 482
DO  - https://doi.org/10.7494/OpMath.2019.39.4.453
UR  - https://doi.org/10.7494/OpMath.2019.39.4.453
AB  - 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.
KW  - PDEs inpainting
KW  - medical imaging
KW  - magnetic particle imaging
KW  - radial curvature image
KW  - anterior surface of a cornea
SN  - 1232-9274
ER  -