Magnetic particle imaging (MPI), in which the nonlinear interaction between internally administered magnetic nanoparticles (MNPs) and electromagnetic waves irradiated from outside of the body is utilized, has attracted attention for its potential to achieve early diagnosis of diseases such as cancer. In MPI, the local magnetic field distribution is scanned, and the magnetization signal from MNPs within a selected region is detected. However, the signal sensitivity and image resolution are degraded by interference from magnetization signals generated by MNPs outside of the selected region, mainly because of imperfections (limited gradients) in the local magnetic field distribution. Here, we propose new methods based on correlation information between the observed signal and the system function–defined as the interaction between the magnetic field distribution and the magnetizing properties of MNPs. We performed numerical analyses and found that, although the images were somewhat blurred, image artifacts could be significantly reduced and accurate images could be reconstructed without the inverse-matrix operation used in conventional image reconstruction methods.