We propose a novel method to reconstruct the optical signal phase information using direct detection. The method is suitable for minimum phase signals and it enables low complexity, low latency, and low tone power operation. Moreover, the proposed method offers low optical complexity solution for the short-reach links compared with the concurrent phase retrieval techniques. We apply the method to M-ary signals with the transmitted power of as low as 3 dBm, and we are able to reach 70 km for 100 Gb/s quadrature phase shift keying (QPSK) system without optical amplification. Our method is based on the single sideband (SSB) and DC-Value property of the minimum phase signal. The SSB and DC-Value properties are iteratively imposed on the amplitude signal in the frequency domain to recover the full complex field from a directly detected optical signal. The normalized mean square error (NMSE) value between the available amplitude information and reconstructed minimum phase signal amplitude decreases after each iteration, providing global minimum convergence. A constant scaling factor is exploited to improve the convergence speed. The scaling factor provides 6 dB, 4.5 dB, and 2.5 dB error vector magnitude (EVM) gains with 4, 5, and 8 iterations, respectively.