1. A method for magnetic resonance imaging, comprising the steps of: operating a magnetic resonance apparatus to acquire magnetic resonance data and entering said magnetic resonance data into a memory representing k-space by sampling k-space using an acquisition method selected from the group consisting of density weighted acquisition and acquisition weighted data acquisition, including undersampling at least one region of k-space with respect to the Nyquist criterion, thereby resulting in non-fulfillment of the Nyquist criterion in said undersampled region, to produce a weighted distribution of data in k-space having a point spread function with substantially no side lobes; and in a processor, reconstructing a magnetic resonance image from the data in k-space using a parallel magnetic resonance imaging method to reduce an influence of said non-fulfillment of the Nyquist criterion on the reconstructed image, and providing said magnetic resonance image at an output of said processor as an image data file.