Inverse Problems
- Office : Building N13(#710)
- Tel : +82-42-821-1737
- E-mail : sungwhan@hanbat.ac.kr
Inverse problems appear in several fields, including medical imaging, image processing, mathematical finance, astronomy, geophysics, nondestructive material testing and sub-surface prospecting. For example, if you know the internal structure of an object, it is relatively straightforward to determine what an X-ray of that object will look like
An inverse problem is the reverse of this; it is the task of using the system’s behaviour to calculate its internal parameters. For example, by taking multiple X-rays at multiple angles, it is possible (in a process known as tomography) to calculate the internal structure of the object. This is the inverse problem of Computerized Tomography. In particular, I have been interested in various inverse problems which occur in Electrical Impedance/Capacitance Tomography and Computerized Tomography, accomplished several mathematical results and reconstruction algorithms for them
Publications
- Sungwhan Kim et al, A Calderon problem with frequency-differential data in dispersive media, Proceedings of the AMS(SCI) (2016)
- Sungwhan Kim et al, A new projection-based iterative image reconstruction algorithm for dual-energy computed tomography, Inverse Problems in Science and Engineering(SCI) (2015)
- Sungwhan Kim et al, Algebraic correction for metal artifact reduction in computed tomography, J. KSIAM, 18 (2014), No. 2, 157-166.
- Sungwhan Kim et al, Reconstructing small perturbations in electrical admittivity at low frequencies, Inverse Problems(SCI), 30 (2014), 035006(18pp).
- Sungwhan Kim et al, “On a Calderon problem in frequency differential electrical impedance tomography”, SIAM J. Math. Anal. (SCI), 45(2013), N0.5, pp.2700-2709.
- Sungwhan Kim et al, “Projective electrical impedance reconstruction with two measurements”, SIAM J. on Applied Math. (SCI), 73(2013), No.4, pp.1659-1675.
- Sungwhan Kim, “Assessment of breast tumor size in electrical im[edance scanning” Inverse Problems(SCI), 28(2012), 025004(13pp).
- Sungwhan Kim et al, “Asymtotic analysis of the membrane structure to sensitivity of frequency-difference electrical impedance tomography” Inverse Problems(SCI), 28(2012), 084002(26pp).
- Sungwhan Kim, “A new alternative elliptic PDE in EIT Imaging” Bull. Korean Math. Soc.(SCIE), 49(2012)
Patent
- APPARATUS AND METHOD FOR COMPUTED TOMOGRAPHY IMAGE PROCESSING.(10-2014-0148888)
- APPARATUS AND METHOD FOR COMPUTERIZED TOMOGRAPHY IMAGE PROCESSING (10-2014-0009036)