Tomography of fusion plasmas is widely applied in order to improve knowledge of plasma emissivity distributions although it is challenging due to sparse spatial resolution of the measured plasma projections. An optimised version of robust and fast tomography algorithm based on Tikhonov regularisation constrained to Minimum Fisher Information is presented in this contribution. A new regularisation matrix enforcing preferential emissivity smoothness along magnetic flux surfaces is introduced. The paper also details application of advanced numerical methods leading to substantial decrease in computation time. Subsequent implementation of fast presolvers of the inverse problem further contributed to the algorithm efficiency and also improved stability of the tomography reconstruction. Finally, reliability and performance of the tomography algorithm is exemplified on reconstruction of soft X-ray data evolution following tungsten ablation into plasma of the JET tokamak. The resulting reconstruction speed is compared to other referenced tomography algorithms.