The tensor-based theory of multidimensional x-space MPI provides useful insight into MPI image reconstruction. Using this theory, it was shown that x-space MPI images with isotropic resolution can be achieved by scanning in two orthogonal directions separately and combining the resulting images. In this work, we propose an x-space image reconstruction that resolves the multidimensional image tensor, allowing us to reconstruct the isotropic MPI image for the Lissajous trajectory. The proposed method takes advantage of the self-crossing property of the Lissajous trajectory.