In magnetic confinement fusion devices, velocity-space tomography of fast-ion velocity distribution function is crucial for investigating fast-ion distribution and transport. In the neutral beam injection (NBI) and ion cyclotron resonance heating (ICRF) synergistic heating experiments in Experimental Advanced Superconducting Tokamak (EAST), high-energy particles with energy exceeding the particle energy in NBI are observed. Simulations of synergistic effect on fast-ion velocity distribution function given by TRANSP also show the existence of particles with energy higher than the particle energy in NBI. To investigate the behaviors of fast ion distribution and calculate the velocity distribution functions under different heating conditions, the first-order Tikhonov regularization tomographic inversion method with higher inversion accuracy is introduced by comparing various regularization techniques. The limitations of the dual-view fast-ion D _α(FIDA) diagnostic measurements in velocity space are addressed by incorporating prior information such as null measurement and the known peaks and effectively mitigate the occurrence of artifacts. This method is first employed in the case of NBI heating. The NBI peak is successfully reconstructed at the expected location in velocity space, which shows significant improvement in the inversion results. In order to further validate the synergistic effect of NBI-ICRF heating and study the mechanism of fast ion distribution under synergistic heating, the combination of FIDA and neutron emission spectrometer (NES) is applied to the first-order Tikhonov regularization tomographic inversion method for enhancing the coverage of velocity space, through which the issue of artifacts in the inversion results is significantly improved, and thus the precision of the obtained fast-ion velocity distribution functions is enhanced. Based on the benefit described above, the method of combining NES diagnosis and FIDA diagnosis is used to obtain fast-ion velocity distribution functions in the NBI and ICRF synergistic heating discharge. The synergistic heating effect is manifested in the fast-ion velocity distribution. The availability of this inversion method in reconstructing fast-ion velocity distribution functions during high-performance operation of NBI-ICRF synergistic heating in the EAST experiment is confirmed. In the next-step EAST research, high performance discharge will demand more efficiency NBI and ICRF synergistic heating, the present work builds the stage for investigating the underlying mechanism of synergistic heating and the intricate behaviors associated with fast ion distribution and transport.