This work presents the Gaussian process tomography (GPT) based on Bayesian data analysis and its applications in soft x-ray (SXR) and absolute extreme ultraviolet spectroscopy (AXUV) diagnostics on experimental advanced superconducting tokamak (EAST). This is the first application of the GPT method in the AXUV diagnostic system in fusion devices. It is found that even if only horizontal detector arrays are used to reconstruct the two-dimensional (2D) distribution of SXR and AXUV emissivity fields, the GPT method performs robustly and extremely fast, which enables the GPT method to provide real-time feedback on impurity transport and fast magnetohydrodynamics (MHD) events. By reconstructing SXR emissivity in the poloidal cross section on EAST, an m/n = 1/1 internal kink mode has been observed, and the plasma redistribution due to the kink mode is clearly visible in the reconstructions, where m is the poloidal mode number and n is the toroidal mode number. Sawtooth-like internal disruptions extended throughout the entire plasma core and mainly driven by the m/n = 2/1 mode have been acquired. During the sawtooth-like internal disruption crash phase, the conversion from an m = 2 mode to an m = 1 mode is observed. Using the reconstructed AXUV emissivity field we were able to observe the process of impurity accumulated in the plasma core and the mitigation of core impurity due to neon injection in the plasma edge. The data from all other diagnostics involved in the analysis shows that the reconstructions from AXUV measurements are reliable.