Quantitative susceptibility mapping (QSM) uses the phase data in magnetic resonance signal to visualize a three dimensional susceptibility distribution by solving the magnetic field to susceptibility inverse problem. Due to the presence of zeros of the integration kernel in the frequency domain, QSM is an ill-posed inverse problem. Although numerous regularization based models have been proposed to overcome this problem, the incompatibility in the field data, which leads to deterioration of the recovery, has not received enough attention. In this talk, we show that the data acquisition process of QSM inherently generates a harmonic incompatibility in the measured local field. Based on such discovery, we propose the harmonic incompatibility removal (HIRE) susceptibility reconstruction models. Experimental results show that the proposed HIRE models achieve better performance than the existing single system regularization based approaches.