Takaaki Nara

Osaka Electro-Communication University, Edo, Tōkyō, Japan

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Publications (66)47.22 Total impact

  • ECS Transactions 02/2015; 65(1):219-226. DOI:10.1149/06501.0219ecst
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    ABSTRACT: This paper deals with the problem of finding poles of rational functions from function values on open curves in the complex plane. For this problem, Nara and Ando recently proposed an algorithm that reduces the problem to a system of linear equations through contour integration. The main aim of this paper is to analyze and improve this algorithm by giving a new interpretation to the algorithm in terms of orthogonal polynomials. It is demonstrated that the system of linear equations is not always uniquely solvable and that this difficulty can be remedied by doubling the number of the linear equations. Moreover, to cope with discretization errors caused by numerical integration, we introduce new polynomials similar, in spirit, to discrete orthogonal polynomials, which yield an algorithm free from discretization errors.
    Journal of Computational and Applied Mathematics 01/2015; 273:326–345. DOI:10.1016/j.cam.2014.05.028 · 1.08 Impact Factor
  • Akihiro Chiba, Takaaki Nara
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    ABSTRACT: This paper presents a novel method for the localization of a passive radio frequency identification (RFID) tag in a 2-D space. First, we show that the position of the tag can be estimated as the intersection of two orthogonal lines, which are determined by the weighted integrals of the magnetic flux density created by the tag. To measure them, we developed a square magnetic sensor composed of six coils: four rectangular coils, a set of four bow-tie-shaped coils connected in series, and a square coil. Using this sensor with side lengths of 200 mm, an RFID tag was localized in a 180 mm square domain with an average error of 5.1 mm. Using the sensor with side lengths of 400 mm, the RFID tag was also localized in a 300 mm square domain with an average error of 1.8 mm.
    IEEE Transactions on Magnetics 09/2014; 50(9):1-8. DOI:10.1109/TMAG.2014.2320693 · 1.21 Impact Factor
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    Shigeru Ando, Takaaki Nara, Toru Kurihara
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    ABSTRACT: Spatial filtering velocimetry was proposed in 1963 by Ator as a velocity-sensing technique for aerial camera-control systems. The total intensity of a moving surface is observed through a set of parallel-slit reticles, resulting in a narrow-band temporal signal whose frequency is directly proportional to the image velocity. However, even despite its historical importance and inherent technical advantages, the mathematical formulation of this technique is only valid when infinite-length observation in both space and time is possible, which causes significant errors in most applications where a small receptive window and high resolution in both axes are desired. In this study, we apply a novel mathematical technique, the weighted integral method, to solve this problem, and obtain exact sensing schemes and algorithms for finite (arbitrarily small but non-zero) size reticles and short-time estimation. Practical considerations for utilizing these schemes are also explored both theoretically and experimentally.
    Measurement Science and Technology 08/2014; 25(8):085001. DOI:10.1088/0957-0233/25/8/085001 · 1.35 Impact Factor
  • T. Nara, M. Fujieda, Y. Gotoh
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    ABSTRACT: For non-destructive inspection of ferromagnetic pipes using magnetic flux leakage (MFL), a sensor consisting of two coils to measure the discrete Fourier sine and cosine coefficients of MFL is developed. The position of a crack in a pipe can be estimated from the squared sum and the ratio of the voltages induced in the two coils. Each coil has sixteen elemental coils with 78 permalloy cores which are placed along a circle with a radius of 6.3 mm and connected in series. The number of turns comprising an elemental coil at an angle ϕ is proportional to sinϕ in one coil and proportional to cosϕ in the other. It was experimentally shown that a circular crack 4 mm in diameter in a ferromagnetic pipe with diameter 21.6 mm was localized. The proposed structure is suitable for narrow pipe inspection where the sensitivity of our previous sensor composed of two coaxial crescent-shaped coils decreases.
    Journal of Applied Physics 04/2014; 115(17). DOI:10.1063/1.4863805 · 2.19 Impact Factor
  • T. Nara, W. Ito
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    ABSTRACT: Euler's equation provides us with a system of linear equations for localizing a magnetic dipole from measurements of the magnetic field and its gradients. However, so far, the condition for the coefficient matrix of the linear equations to be singular has not been shown. In this paper, we show that the matrix is singular if and only if the dipole moment is perpendicular to the dipole position vector, where the observation point is set at the origin. Moreover, we show that, even in this case, the true position can be uniquely reconstructed by using the Moore-Penrose generalized inverse of the gradient tensor.
    Journal of Applied Physics 04/2014; 115(17). DOI:10.1063/1.4861675 · 2.19 Impact Factor
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    ABSTRACT: This paper presents an algebraic reconstruction method for dipole-quadrupole sources using magnetoencephalography data. Compared to the conventional methods with the equivalent current dipoles source model, our method can more accurately reconstruct two close, oppositely directed sources. Numerical simulations show that two sources on both sides of the longitudinal fissure of cerebrum are stably estimated. The method is verified using a quadrupolar source phantom, which is composed of two isosceles-triangle-coils with parallel bases.
    Journal of Applied Physics 04/2014; 115(17). DOI:10.1063/1.4869066 · 2.19 Impact Factor
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    Shigeru Ando, Takaaki Nara, Tsukassa Levy
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    ABSTRACT: Wave source localization from a sensor array has long been the most active research topics in both theory and application. In this paper, an explicit and time-domain inversion method for the direction and distance of a monopole source from a circular array is proposed. The approach is based on a mathematical technique, the weighted integral method, for signal/source parameter estimation. It begins with an exact form of the source-constraint partial differential equation that describes the unilateral propagation of wide-band waves from a single source, and leads to exact algebraic equations that include circular Fourier coefficients (phase mode measurements) as their coefficients. From them, nearly closed-form, single-shot and multishot algorithms are obtained that is suitable for use with band-pass/differential filter banks. Numerical evaluation and several experimental results obtained using a 16-element circular microphone array are presented to verify the validity of the proposed method.
    The Journal of the Acoustical Society of America 10/2013; 134(4):2799-2813. DOI:10.1121/1.4820896 · 1.56 Impact Factor
  • Abdellatif El Badia, Takaaki Nara
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    ABSTRACT: In this paper, we investigate an inverse source problem of the time harmonic Maxwell equations at a fixed frequency, where the source consists of multiple point dipoles. An algebraic algorithm is proposed to identify the number, locations and moments of the dipoles from boundary measurements of tangential components of the electric and magnetic fields. Also, a Hölder stability result is shown. The proposed algorithm is numerically verified.
    Inverse Problems 12/2012; 29(1):015007. DOI:10.1088/0266-5611/29/1/015007 · 1.80 Impact Factor
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    ABSTRACT: This paper presents a novel algorithm and sensor for estimating the position of a magnetic dipole. By transforming Euler's equation of degree -3 into an integral form, we have linear equations relating the dipole position to the surface integrals of the magnetic flux densities on a cube. To measure all the quantities required in the linear equations, we develop a cubic sensor with a side length of 50 mm which consists of 18 coils. We show that the coefficient matrix of the linear equations is symmetric and traceless, which can be used to improve localization accuracy. By performing the nonlinear least squares method with the initial solution given by the proposed method, the average and maximum error are 8.3 and 17.5 mm, respectively, in the range of 500 mm.
    IEEE Transactions on Magnetics 11/2012; 48(11):4444-4447. DOI:10.1109/TMAG.2012.2196418 · 1.21 Impact Factor
  • Takaaki Nara
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    ABSTRACT: This paper presents a method for identifying the general-order poles of a meromorphic function algebraically from its values on the unit circle, which has various applications in inverse source problems in potential analysis. First, we derive a system of Dth-degree equations for N distinct poles zn of order Dn, where n = 1, 2, ..., N and D = max 1 ≤ n ≤ N{Dn}. Then, we transform these equations into linear equations for the coefficients of the Nth-degree equation whose roots are zn so that the poles are obtained algebraically from data. The obtained poles can be used as an initial solution for iterative algorithms. A method for estimating the order Dn of each pole is also proposed and is numerically verified.
    Inverse Problems 01/2012; 28(2):025008. DOI:10.1088/0266-5611/28/2/025008 · 1.80 Impact Factor
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    ABSTRACT: This paper presents a method for estimating the position of a radio-frequency identification (RFID) tag in two-dimensional (2D) space. A low-frequency (135 kHz), passive RFID tag with a loop antenna transmits its ID number to the tag reader by electromagnetic induction. This study reveals that the radial distance and the azimuth of the RFID tag in a 2D plane can be determined from the absolute value and phase of the first-order Fourier coefficient of the magnetic flux density generated by the tag. The authors develop a sensor unit that consists of four coils: two special coils that generate electromotive forces that are proportional to the first-order Fourier cosine and sine coefficients and two conventional loop coils. Using the developed sensor, a 29-mm-diameter disk-shaped RFID tag can be localized with a maximum (average) error of 18 mm (5 mm) within a circular domain of radius 140 mm.
    01/2012; 5(4):226-232. DOI:10.9746/jcmsi.5.226
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    Takaaki Nara
    Magnetoencephalography, 11/2011; , ISBN: 978-953-307-255-5
  • Abdellatif El Badia, Takaaki Nara
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    ABSTRACT: The inverse source problem of the Helmholtz equation in an interior domain is investigated. We show the uniqueness and local stability, where the source consists of multiple point sources. An algebraic algorithm is proposed to identify the number, locations and intensities of the point sources from boundary measurements. Uniqueness and non-uniqueness results for some distributed sources are also established. The proposed method is verified numerically.
    Inverse Problems 09/2011; 27(10):105001. DOI:10.1088/0266-5611/27/10/105001 · 1.80 Impact Factor
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    ABSTRACT: A simple sensor for magnetic flux leakage methods of detecting cracks on the surfaces of ferromagnetic pipes is proposed. We show that the crack position can be determined by the Fourier coefficients of the leakage magnetic flux density on a circle inside the pipe in the pipe cross-sectional plane. Coils that directly output the Fourier cosine and sine coefficients were made. The experimental results showed that, using only these two coils rather than dozens of magnetic sensors, the center position of a crack on the inside/outside surface of the pipe could be localized.
    Journal of Applied Physics 04/2011; 109(7). DOI:10.1063/1.3535546 · 2.19 Impact Factor
  • T. Nara, H. Watanabe, W. Ito
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    ABSTRACT: This paper presents a novel algorithm and sensor for estimating the position of a magnetic dipole irrespective of its posture in 3D space. We transform the so-called Euler equation that is the linear equation relating the dipole position to the magnetic field and its gradients into the equation that the divergence of a certain vector field is zero. Then, we derive its weak form using the Gauss theorem. As a result, the dipole positions can be obtained as the solution to linear equations in which the coefficients to be measured are the differences of the surface integrals of the magnetic field, not the gradients of the magnetic field as in Euler's equation. A cubic sensor consisting of 18 coils for measuring those quantities is developed. The method is verified experimentally.
    SICE Annual Conference (SICE), 2011 Proceedings of; 01/2011
  • Akihiro CHIBA, Takaaki NARA
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    ABSTRACT: This paper presents a novel method for the localization of an RFID tag in two-dimensional (2D) space, which can be used in location-aware systems. First, in a 2D square domain inside which an RFID tag is freely placed and moved, we show that a line on which the RFID tag exists can be estimated from the weighted integrals of the magnetic field created by the tag along the boundary of the domain. Then, for measuring them, we develop a square-shaped magnetic sensor composed of three coils only: two pairs of oppositely-wound rectangle coils connected in series on the parallel sides of the squared domain, and four bow-tie-shaped coils connected in series on all sides. The average localization error is 5.9 mm in the 160 mm × 160 mm domain.
    SICE Annual Conference (SICE), 2011 Proceedings of; 01/2011
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    ABSTRACT: In this paper, we present a method for reconstructing the dipole sources inside the human brain from radial Magnetoencephalography data measured on the part of the boundary which encloses the source. Combining the proposed method with the direct method provides a good initial solution for an optimization-based algorithm. The method is verified with the numerical simulations, phantom experiments, and a somatosensory evoked field data analysis.
    01/2011; 3. DOI:10.14495/jsiaml.3.65
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    ABSTRACT: This paper presents a method for estimating the 2D position of a magnetic dipole from measurements of the first order Fourier coefficients of its magnetic flux density on a circle with an arbitrary radius. It is proved that the azimuth of the dipole is equal to the phase of the first order complex Fourier coefficient. The method is verified by experiments using coils which can directly measure the Fourier coefficients.
  • Abdellatif El Badia, Takaaki Nara
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    ABSTRACT: In this paper, we show the uniqueness and local stability of an inverse source problem for the quasi-static Maxwell equation in a layered domain, where the source consists of multiple point dipoles. Also, an algebraic algorithm is proposed to identify the number, locations, and moments of the dipoles from boundary measurements of tangential components of the electric and magnetic fields. The proposed algorithm is numerically verified.
    Journal of Inverse and Ill-Posed Problems 01/2010; 18(7). DOI:10.1515/jiip.2011.002 · 0.59 Impact Factor

Publication Stats

418 Citations
47.22 Total Impact Points

Institutions

  • 2008–2013
    • Osaka Electro-Communication University
      Edo, Tōkyō, Japan
  • 2008–2012
    • The University of Electro-Communications
      • Department of Mechanical Engineering and Intelligent Systems
      Edo, Tōkyō, Japan
  • 2004–2009
    • Kyoto Prefectural University of Medicine
      • Department of Dermatology
      Kioto, Kyōto, Japan
  • 2000–2007
    • The University of Tokyo
      • Department of Interdisciplinary Information Studies
      Tōkyō, Japan
  • 2002–2006
    • Saitama University
      • Department of Mechanical Engineering
      Saitama, Saitama-ken, Japan
    • National Institute of Informatics
      Edo, Tōkyō, Japan