Magnetic Particle Imaging (MPI) is a recently introduced medical imaging modality that promises high sensitivity, high resolution and real-time ability by imaging the spatial distribution of super-paramagnetic iron-oxide nanoparticles. The reconstruction techniques can be categorized into frequency and x-space reconstruction. In this book, a comparison between both techniques is made based on a simulation study. The x-space reconstruction technique using the Lissajous trajectories is presented for various parameters of an ideal scanner. Furthermore, the deconvolution process for the x-space reconstruction is performed with two techniques, the Tikhonov and the Wiener deconvolution. Frequency reconstruction and x-space reconstruction are compared in terms of different setups regarding the density of the trajectory, gradient strength and sampling frequency for an ideal scanner and a realistic scanner with classical coil geometry. The advantages and disadvantages of both reconstruction techniques are analyzed in detail.