Sparse-Data CT Image Reconstruction Using Tikhonov-Phillips Regularization and GVC: Application to Plasma Images

摘要

The Tikhonov-Phillips regularization and the mini- mum generalized cross validation (GCV) criteria are ap- plied to computer tomography (CT) which has sparse data and noise to optimize their reconstructed images. Using plasma images having sparse (several hundred) projection data and pixels, experimental data-processing and simula- tions of the method are carried out. Mathematical concepts of image reconstruction, including the Fourier base and expansion coefficients, are examined. The results show that the differential operator of the Phillips equation improves the base system of an image (notably its low-frequency waves), and prevents deterioration of the data. The results also show that the GCV appropriately indicates the image compression, as a criterion of choosing the regularization parameters and the evaluation functions. The effectiveness of this method (a linear-algebraic solution) on a sparse-data CT has been confirmed experimentally.