Edge enhancement with incoherent illumination is an important research branch of optical imaging and information processing, which presents valuable potential application in target recognition, biomedical microscopy, optical defects detection, optical localization and so on. However, the incoherent optical imaging and information processing system is linear invariable of light intensity transfer and there is not an accurate correspondence spatial frequency plane of object complex-amplitude, thus it is limited to obtain edge enhancement imaging by spatial filter in incoherent system. We proposed a computational incoherent edge enhancement imaging based on self-interference digital holography (SIDH). SIDH offers the incoherent object complex-value holograms which is consisted of the incoherent superimposing point spread holograms. The phase of the point spread holograms not only code the depth information of corresponding object-point, but also the difference of the two interference beams and the aberration introduced by recording scheme. The characteristics of incoherent self-interference hologram are employed to utilize edge enhancements and adaptive aberration correction during reconstruction, thus the Laguerre-Gaussian vortex angle spectrum algorithm of SIDH hologram are modified and developed, simultaneous regulating both amplitude and phase in the reconstruction process. Both experimental results demonstrate our method exhibits better performances for edge extraction, background noise can be well suppressed, edge becomes sharper and high contrast. The proposal has also been verified that it can be used for direction-optional edge enhancement, edge enhancement with adaptive aberration correction and edge enhancement imaging of different depth objects simultaneously.