DSP-enhanced intensity-modulation direct-detection (IM/DD) systems can support up to 56 Gb/s over 100 km signal transmissions at C-band. To achieve higher data rates and longer transmission distances, we propose data-aided iterative algorithm (DIA) and decision-directed DIA (DD-DIA) to digitally mitigate signal-signal beating interference (SSBI) without requiring any modifications to physical layer structures. DIA utilizes pilot symbols with uniformly spaced insertions to relax the modified Gerchberg-Saxton (G-S) algorithms that suffer from the local optimum problem. To further improve the symbol error rate (SER) performance and convergence speed, DD-DIA introduces a decision process to generate pseudo-pilots. We numerically compare DIA with other algorithms and find that DIA can recover signals subject to large fiber dispersions corresponding to which conventional IA and Volterra filter (VF) fail, while DD-DIA significantly accelerates the convergence speed and improves the reconstruction performance compared with DIA, it can support 100-Gb/s PAM4 over 400-km IM/DD transmissions within just 50 iterations. Two orders of magnitude reductions in SER is observed for 100 Gb/s PAM4 signal transmission over 100-km SSMFs. Compared with conventional IA, the proposed techniques have higher convergence speeds, better global optimum features and large tolerances to physical model errors. In particular, DD-DIA results in larger optical signal-to-noise ratio (OSNR)/ received optical power (ROP) improvement, higher transmission capacities and less computational complexity. DD-DIA is a promising algorithm for efficiently reconstructing 2-dimensional optical field for conventional IM/DD optical transmission systems.