Regularization of soft-X-ray imaging in the DIII-D tokamak

An image inversion scheme for the soft-X-ray imaging system (SXRIS) diagnostic at the DIII-D tokamak is developed to obtain the local soft-X-ray emission at a poloidal cross-section from the spatially line-integrated image taken by the SXRIS camera. The scheme uses the Tikhonov regularization method since the inversion problem is generally ill-posed. The regularization technique uses the generalized singular value decomposition (GSVD) to determine a solution that depends on a free regularization parameter. The latter has to be chosen carefully, and the so-called L-curve method to find the optimum regularization parameter is outlined. A representative test image is used to study the properties of the inversion scheme with respect to inversion accuracy, amount/strength of regularization, image noise and image resolution. The optimum inversion parameters are identified, while the L-curve method successfully computes the optimum regularization parameter. Noise is found to be the most limiting issue, but sufficient regularization is still possible at noise to signal ratios up to 10%–15%. Finally, the inversion scheme is applied to measured SXRIS data and the line-integrated SXRIS image is successfully inverted.