B.J. Peterson

N. Iwama

Y. Hosoda

National Institute for Fusion Science (NIFS-Repository)

0.001Vacuum Vessel0.0001a L---,-..L-J---'--L..L..l-L.1_-,--,---,--J.....L-l..u..L_..L--.J'--'-I.....W..JUJ10.5I : GCV I-k-MSEFig. 1. Layout of two 20-channel fan-beam cameras inthe semi-tangential cross section with 3.5U and4-0 ports.Fig. 2. Reconstructed profile during radiative collapsein the triangular region; Shot 28961,2.162 sec.§ 13. Image Reconstruction of LHD Plasma inBolometer TomographyNE(r) =L Wi (r)(a/u; S)C-1l{i=lThe 2-D distribution measurement of radiation bymeans ofAXUV silicon photodiode arrays [l,2] wasdeveloped in adopting a numerical tool of image recon-struction of computed tomography. With respect to thecamera system amounted in a semi-tangential cross sec-tion of LHD (Fig. 1), the Tikhonov-Phillips regulariza-tion method for inversion [3] was applied to detectorsignals. A square region which covers the triangularplasma region presumed from the magnetic surface config-uration was devided to 32x32 pixels, and the projectionmatrix that was geometrically calculated by taking intoaccount the sight volumes of detectors [1] was used.Given the projection matrix L and the M-dimensionaldata vector S (M=40), the image vector estimate E withthe Laplacian smoothing operator C is written in a formof series expansion; that is, we haveIwama, N. (School of Informatics, Daido Institute ofTechnology)Hosoda, Y. (Dept. Information Science, Fukui Univ.)Peterson, B.J.Here Ui , Vi and a; are the singular vectors and the singularvalues of LC-1, and wJr) = (l + is a lowpassfilter function with the regularization parameter r; we haveN=min(M,K) for the pixel number K. In order to neglectthe pixels on the outside of the plasma region innumerical processing, the vector E was reduced indimension, and the corresponding columns of L and therelated columns and rows of C were omitted.A result of analyzing the camera signals is shown inFigs. 2 and 3. The obtained contour map in Fig. 2 exhib-its the radiation intensity distribution in an asymmetricradiative collapse of NBI heated plasma [2]. This map wasobtained for the r value that minimized the generalizedcross validation (GCV), which is written asAs a function of r , the GCV behaved as plotted inFig. 3 in this example, while the mean square error E\r)of the chord-integrated value LE(nin fitting to the detec-tor outputs S was monotonically decreased with r. This. 2behavior of E (r) was favorable, endorsed by the goodfittings of all the chord-integrated values without largeerrors.Regularization Parameter rFig. 3. Changes of GCV(r) and E2 Cy) (MSE) with r.GCVCr) was minimized for r=1.0xl0-4•References1) Kostriukov, A.Yu., Liu, Y. et aI., Ann. Rep. NIFS (2001-2002) 157.2) Peterson, BJ. et aI., Ann. Rep. NIFS (2001-2002) 55.3) Terasaki, N., Iwama, N. and Hosoda, Y., Trans. IEICEJ81·D·II, (1998) 93.162

Image Reconstruction of LHD Plasma in Bolometer Tomography

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