Combining noncoherent detection (NCD) with polar codes is a promising way to improve the performance of polar-coded systems in presence of imperfect channel state information. This letter proposes a novel NCD architecture for polar-coded systems by exploiting information feedback and reconstruction. Specifically, extra low-complexity signal processing steps are merged into the conventional polar-coded scheme with NCD, yielding low detection complexity that is crucial for resource-limited systems. Moreover, a polar-coded NCD algorithm is proposed via the information feedback and reconstruction. Simulation results prove that our proposed algorithm outperforms conventional NCD algorithms in terms of bit error rate and block error rate. Finally, the complexity of the proposed NCD algorithm is analyzed in detail.