In this Letter, we propose a low-complexity adaptive multipath interference (MPI) and channel noise mitigation (AMCM) scheme in the receiver digital signal processing (DSP) for bandwidth-limited intensity modulation and direct detection (IM/DD) transmission systems. Following channel equalization, MPI and channel noise are distributed in the low- and high-frequency parts, respectively, and exhibit the characteristics of bandstop filtering. The proposed AMCM is designed based on optimized detection, which incorporates an adaptive bandpass filter (BPF) and a log-maximum a posteriori estimation with a lookup table-based fixed number of surviving states (LUT-based FS-MAP) decoder. The adaptive BPF is capable of mitigating the MPI and channel noise based on spectral distribution. Moreover, the LUT-based FS-MAP decoder can eliminate intersymbol interference (ISI) introduced by the BPF. The proposed AMCM is implemented in an O-band 56-Gbaud IM/DD optical 4-level pulse amplitude modulation (PAM-4) system with a 10.7-GHz bandwidth over a 10-km standard single-mode fiber with different linewidths. The results demonstrate that the proposed AMCM scheme can enhance signal-to-interference ratio (SIR) tolerance to 11 dB with only three real-valued multiplications per symbol, achieving a 7% hard-decision forward error correction threshold. To the best of our knowledge, for the first time, this represents the inaugural instance of optimized detection being employed for MPI mitigation.