Tomographic Inversion Technique Using Orthogonal Basis Patterns

Abstract

Tomographic reconstruction of the emission profile is a typical ill-posed inversion problem. It becomes troublesome in fusion plasma diagnostics because the possible location/direction of the observation is quite limited. In order to overcome the difficulty, many techniques have been developed. Among them, series expansion methods are based on decomposing the emission profile with orthogonal or nearly orthogonal basis patterns. Since it is possible to ignore the surplus components with higher spatial frequency, this type of method is robust against noise issues. Two topics are discussed in this article. The first issue is the comparison of the basis systems themselves. Conventional one of Fourier-Bessel and a new one of the so-called Laplacian eigen function are compared from the viewpoint of the capability of expressing the patterns that appear in the fusion plasma experiment. The second issue is the application to the tangential viewing imaging system. It is shown that, even from the limited information, tomographic reconstruction can be adequately performed with appropriate use of the regularization, especially with the use of the L1 regularization.

Resolving the fast ion distribution from imaging neutral particle analyzer measurements

“…Recently, a new tomographic inversion method [53] based on L1 regularization or lasso regularization using conventional Fourier-Bessel eigenfunctions or the Laplacian eigenfunctions has shown success in overcoming the noise problems in the tangential viewing imaging data [54]. The success stimulates the interest in the development of similar methods for the velocity-space tomography.…”

MHD Equilibrium Reconstruction Using the Visible Light Tomographic Method with Laplacian Eigenfunction

“…Having obtained a i , we can easily calculate the reconstructed image f using Eq. (7). The Fourier basis is generally used in image processing as a series expansion approximation of an image.…”

“…K. Yamasaki et al [6] proposed a method to optimize the Fourier-Bessel expansion coefficients precisely. S. Ohdachi et al [7] compared the basis patterns between the Fourier-Bessel and Laplacian eigenfunction and showed the validity of the L 1 regularization.…”

New tomographic reconstruction technique based on Laplacian eigenfunction

“…The patterns are aligned with the magnetic surface calculated on the magnetic surface. The orthogonality is kept almost the same, having a near-orthogonal nature, even for the non-circular plasma cross-sections [9]. However, the requirement of flux surfaces is then always required.…”

“…Ohdachi et al discussed the new pattern of the LEF constructed on the flux coordinate system. In such a case, the pattern is not exactly orthogonal but is near-orthogonal [9]. However, in principle, the new pattern based on the LEF is intrinsically independent to the flux surface shape and it does not require the flux surface information to construct patterns.…”