As an indirect and computational imaging approach, imaging reconstruction efficiency is critical for ghost imaging (GI). Here, we compare different GI algorithms, including logarithmic GI and exponential GI we proposed, by numerically analysing their imaging reconstruction efficiency and error tolerance. Simulation results show that compressive GI algorithm has the highest reconstruction efficiency due to its global optimization property. Error tolerance studies further manifest that compressive GI and exponential GI are sensitive to the error ratio. By replacing the bucket input of compressive GI with different bucket object signal functions, we integrate compressive GI with other GI algorithms and discuss their imaging efficiency. With the combination between the differential GI (or normalized GI) and compressive GI, both reconstruction efficiency and error tolerance will present the best performance. Moreover, an optical encryption is proposed by combining logarithmic GI, exponential GI and compressive GI, which can enhance the encryption security based on GI principle.