A method for accelerating data acquisition in MRI with N-dimensional spatial encoding has a first method step in which a transverse magnetization within an imaged object volume is prepared having a non-linear phase distribution. Primary spatial encoding is thereby effected through application of switched magnetic fields. Two or more RF receivers are used to simultaneously record MR signals originating from the imaged object volume, wherein, for each RF receiver, an N-dimensional data matrix is recorded which is undersampled by a factor Ri per selected k-space direction. Data points belonging to a k-space matrix which were not recoded by a selected acquisition schema are reconstructed using a parallel imaging method, wherein reference information concerning receiver coil sensitivities is extracted from a phase-scrambled reconstruction of the undersampled data matrix. The method generates a high-resolution image free of artifacts in a time-efficient manner by improving data sampling efficiency and thereby reducing overall data acquisition time.