Phase-retrieval (PR) receivers can reconstruct complex-valued signals from two de-correlated intensity measurements, without the assistance of any optical carriers. However, both the calculation complexity with hundreds of iterations and the limited PR accuracy prevent it from being applied to high-speed photonic interconnections. Here we propose and demonstrate a PR receiver based on adaptive intensity transformation, with the capability of both fast convergence and high accuracy. Then we numerically reconstruct 56 GBaud QPSK signals after the 80 km standard single-mode fiber transmission by using our proposed PR receiver with only 50 iterations. In comparison with the recently reported PR receiver with the phase reset, our proposed PR receiver can reduce the required optical signal-to-noise ratio by 1.95 and 1.89 dB, in terms of 20% soft-decision and 7% hard-decision forward-error correction, respectively.