Method for reconstructing a sequence of magnetic resonance images of an object under investigation, comprising the steps of: (a) arranging the object in a magnetic resonance imaging device including at least one radiofrequency receiver coil, subjecting the object to a gradient-echo sequence and collecting a series of sets of image raw data wherein, from each of the sets, one of the MR images of the sequence is to be reconstructed, wherein - each set of image raw data includes a plurality of data samples being generated with a gradient-echo sequence that spatially encodes an MRI signal received with the at least one radiofrequency receiver coil using a non-Cartesian k-space trajectory, - each set of image raw data comprises an undersampled plurality of homogeneously distributed lines in k-space with equivalent spatial frequency content, - each of the lines of each set of image raw data cross the center of k-space and cover a continuous range of spatial frequencies, and - the positions of the lines of each set of image raw data differ in successive sets of image raw data, characterized by the further step of (b) subjecting each set of image raw data of the series of sets of image raw data to a regularized nonlinear inverse reconstruction process to provide the sequence of MR images, wherein the nonlinear inverse reconstruction process is an iterative process which, in each iterative step, solves a regularized linearization of a nonlinear MRI signal equation which maps the unknown spin density of the MR image to be reconstructed from the set of image raw data and the unknown spatial coil sensitivity of the at least one radiofrequency receiver coil to the raw data of the set, thereby providing a simultaneous estimation of the coil sensitivity of the at least one receiver coil and the spin density of the MR image to be reconstructed from the set, wherein the nonlinear inverse reconstruction process includes a regularization, wherein for each of the sets subjected to the nonlinear inverse reconstruction process, except for the temporally first set, the nonlinear inverse reconstruction process uses the spin density of an MR image and the sensitivity of the at least one receiver coil that were reconstructed by subjecting a preceding set of the series of sets of image raw data to the nonlinear inverse reconstruction as a reference for the regularization of the nonlinear inverse reconstruction process. (a) arranging the object in a magnetic resonance imaging device including at least one radiofrequency receiver coil, subjecting the object to a gradient-echo sequence and collecting a series of sets of image raw data wherein, from each of the sets, one of the MR images of the sequence is to be reconstructed, wherein - each set of image raw data includes a plurality of data samples being generated with a gradient-echo sequence that spatially encodes an MRI signal received with the at least one radiofrequency receiver coil using a non-Cartesian k-space trajectory, - each set of image raw data comprises an undersampled plurality of homogeneously distributed lines in k-space with equivalent spatial frequency content, - each of the lines of each set of image raw data cross the center of k-space and cover a continuous range of spatial frequencies, and - the positions of the lines of each set of image raw data differ in successive sets of image raw data, characterized by the further step of - each set of image raw data includes a plurality of data samples being generated with a gradient-echo sequence that spatially encodes an MRI signal received with the at least one radiofrequency receiver coil using a non-Cartesian k-space trajectory, - each set of image raw data comprises an undersampled plurality of homogeneously distributed lines in k-space with equivalent spatial frequency content, - each of the lines of each set of image raw data cross the center of k-space and cover a continuous range of spatial frequencies, and - the positions of the lines of each set of image raw data differ in successive sets of image raw data, (b) subjecting each set of image raw data of the series of sets of image raw data to a regularized nonlinear inverse reconstruction process to provide the sequence of MR images, wherein the nonlinear inverse reconstruction process is an iterative process which, in each iterative step, solves a regularized linearization of a nonlinear MRI signal equation which maps the unknown spin density of the MR image to be reconstructed from the set of image raw data and the unknown spatial coil sensitivity of the at least one radiofrequency receiver coil to the raw data of the set, thereby providing a simultaneous estimation of the coil sensitivity of the at least one receiver coil and the spin density of the MR image to be reconstructed from the set, wherein the nonlinear inverse reconstruction process includes a regularization, wherein for each of the sets subjected to the nonlinear inverse reconstruction process, except for the temporally first set, the nonlinear inverse reconstruction process uses the spin density of an MR image and the sensitivity of the at least one receiver coil that were reconstructed by subjecting a preceding set of the series of sets of image raw data to the nonlinear inverse reconstruction as a reference for the regularization of the nonlinear inverse reconstruction process.