Takashi TAKIGUCHI
@nda.ac.jp
National Defense Academy
Scopus Publications
- Structure of the least square solutions to overdetermined systems and its applications to practical inverse problems
Kenji Hashizume, Makoto Maruya, Takayuki Ochi, Toshiaki Takabatake, Takashi Takiguchi
Japan Journal of Industrial and Applied Mathematics, 2024 - A theoretical study of the algorithm to practicalize CT by G. N. Hounsfield and its applications
Takashi Takiguchi
Japan Journal of Industrial and Applied Mathematics, 2020
In this paper, we give a theoretical justification of the idea by G. N. Hounsfield for the practicalization of the computerized tomography (CT). He developed a device for medical CT, for which he was awarded Nobel Prize for Physiology or Medicine. There being a number of researches concerning Hounsfield’s idea, we give a new stochastic approach to prove that it is theoretically right. We also discuss its applications. - Global uniqueness for the radon transform
Bulletin of the Korean Mathematical Society, 2020 - Ultrasonic tomographic technique and its applications
Takashi Takiguchi
Applied Sciences Switzerland, 2019
X-ray tomography and magnetic resonance imaging (MRI) are excellent techniques for non-destructive or non-invasive inspections, however, they have shotcomings including the expensive cost in both the devices themselves and their protection facilities, the harmful side effects of the X-rays to human bodies and to the environment. In view of this argument, it is necessary to develop new, inexpensive, safe and reliable tomographic techniques, especially in medical imaging and non-destructive inspections. There are new tomographic techniques under development such as optical tomography, photo-acoustic tomography, ultrasonic tomography and so on, from which we take ultrasonic tomography as the topic in this paper. We introduce a review of the known ultrasonic tomographic techniques and discuss their future development. - Representation of the Vortex Sheets in the Perfect Fluid
Takashi Takiguchi
Journal of Mathematical Fluid Mechanics, 2018
We discuss representation of the vortex sheets in the perfect fluid. In the preface of his book, I. Imai claimed “hyperfunction = vortex layer”, the proof of which had not been given. In 2009, K. Uchikoshi-Y. Noro gave a hyperfunctional representation of the vortex layers in the 2-dimensional fluid. Their idea being highly dependent on identifying the two dimensional Euclidean plane with the complex plane, it is difficult to interpret their representation in the real fluid phenomena. Its 3-dimensional extension was also difficult. To solve these problems, we give a new representation of the vortex sheets (or layers) by the real flow velocity vectors, whose other merits are also discussed. - Unique continuation of microlocally analytic functions and their structure
Takashi Takiguchi
Complex Variables and Elliptic Equations, 2014
We study a unique continuation property of microlocally analytic functions. This property depends on the regularity of the functions. In this article, we mainly discuss the unique continuation property of the microlocally analytic quasi-analytic ultradistributions and hyperfunctions, whose relation with their structure is also discussed. - Achievements by Professor Akira Kaneko
Tsutomu Sakurai, Takashi Takiguchi
Complex Variables and Elliptic Equations, 2014
In this article, we review the achievements by Professor Akira Kaneko, who mainly contributed to the continuation of regular solutions to linear partial differential equations and to the theory of hyperfunctions. - Non-uniqueness of the reconstruction for connected and simply connected sets in the plane by their fixed finite projections
Takashi Takiguchi
Acta Mathematica Scientia, 2012 - On the structure of generalized functions
Takashi Takiguchi
Complex Variables and Elliptic Equations, 2009
We study the structure of generalized functions. We introduce the structure theorem for the quasi-analytic ultradistributions. We also discuss the relation between the structure theorem and the generalized unique continuation property. †Dedicated to Professor Luigi Rodino on his 60th birthday. ‡This article is devoted to the special issue ‘Växjö Conference 2008’. - Abel-type integral transforms and the exterior problem for the Radon transform
Tadashi Ohsawa, Takashi Takiguchi
Inverse Problems in Science and Engineering, 2009
In this article, we first discuss inversion methods of the Abel-type integral transforms. It is well known that the support theorem of the Radon transform does not hold unless the function decreases rapidly at infinity. We prove that this support theorem holds for L1 functions if they are radial. The inversion methods of the Abel-type integrals play an important role to prove the support theorem for the radial functions. We also prove inversion formulae of the exterior problems for the Radon transform of the radial functions. - Reconstruction of the measurable sets in the two dimensional plane by two projections
Takashi Takiguchi
Journal of Physics Conference Series, 2007 - Structure of quasi-analytic ultradistributions
Takashi Takiguchi
Publications of the Research Institute for Mathematical Sciences, 2007 - Remarks on modification of Helgason's support theorem. II
Takashi Takiguchi
Proceedings of the Japan Academy Series A Mathematical Sciences, 2001 - Remarks on modification of Helgason's support theorem
T. Takiguchi
Journal of Inverse and Ill Posed Problems, 2000 - The reconstruction of uniquely determined plane sets from two projections
L. HUANG, T. TAKIGUCHI
Journal of Inverse and Ill Posed Problems, 1998 - Radon transform of hyperfunctions and support theorem
Takashi TAKIGUCHI, Akira KANEKO
Hokkaido Mathematical Journal, 1995
