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Magnetic particle imaging (MPI) is an emerging tomographic imaging modality with high spatial and temporal resolution. The image reconstruction in MPI needs to solve an ill-posed inverse problem. Tikhonov regularization is known to solve this kind of problems. However, the traditional Tikhonov regularization (L2 regularization) guides the reconstruction to be over smooth and tends to generate a lot of low-value noise in the background. In this work, we develop an efficient and noise reducing reconstruction method for MPI. We proposed a Gaussian weighted Laplace regularization which assumes that the correlation between any two voxels inside the field of view (FOV) has a non-linear inverse relationship with their spatial distance. Experimental results show proposed method can provide more accurate MPI reconstruction.