Abstract: A method for designing the time dependence function km(t) for a given k-space trajectory km, where m stands for one or multiple of the spatial dimension indices x, y, or z, of a magnetic resonance imaging (=MRI) experiment carried out on an MRI system, wherein the trajectory km is generated by applying a time varying waveform gm(t) of a gradient magnetic field, the method taking into account—the gradient magnitude limit G and—the gradient slew rate limit S of the MRI system, is characterized in that the method further takes into account a given frequency limit F in such a way that the gradient waveform gm(t) does not contain frequency components above the frequency limit F which is characteristic for the gradient hardware of the MRI system. The invention provides a method for designing a time dependence function for a given k-space trajectory, which allows obtaining better quality MRI images.

Abstract: A method for magnetic resonance spectroscopy (=MRS) or magnetic resonance imaging (=MRI) in which an NMR time-domain signal is generated by an excited transverse nuclear magnetization precessing about the applied magnetic field, whereby the RF excitation pulse is adapted to cover a whole range of NMR frequencies of interest present in the object, and time-domain signal acquisition takes place during, or during and after the application of the RF excitation pulse, is characterized in that spectral or image data are reconstructed by a matrix product of a reconstruction matrix and a vector of time-domain signal points, the reconstruction matrix being an inversion of an encoding matrix. An improved method for reconstructing spectral or image data from a time-domain signal is thereby provided which is more versatile than conventional Fourier transform.

Abstract: A method for designing the time dependence function km(t) for a given k-space trajectory km, where m stands for one or multiple of the spatial dimension indices x, y, or z, of a magnetic resonance imaging (=MRI) experiment carried out on an MRI system, wherein the trajectory km is generated by applying a time varying waveform gm(t) of a gradient magnetic field, the method taking into account—the gradient magnitude limit G and—the gradient slew rate limit S of the MRI system, is characterized in that the method further takes into account a given frequency limit F in such a way that the gradient waveform gm(t) does not contain frequency components above the frequency limit F which is characteristic for the gradient hardware of the MRI system. The invention provides a method for designing a time dependence function for a given k-space trajectory, which allows obtaining better quality MRI images.