We demonstrate a series of experiments on imaging through both stationary aberrating media and moving aberrating media by computational ghost imaging (CGI). An incoherent LED light source is used instead of the common pseudothermal light source (laser light passing through a rotating ground glass). A digital micromirror device is used as a simple spatial light modulator to perform CGI. Moreover, a digital filtering method is introduced to improve imaging quality through moving aberrating media. This imaging modality may have potential applications in medicine and astronomy.