Method and apparatus for performing accelerated magnetic resonance imaging with reduced oversampling at low spatial frequencies

A computer-implemented method of computing a trajectory in k-space to be used for sample acquisition in magnetic resonance imaging, the method comprising the steps of:

• i. determining, or receiving from a user input, a number Nc≤1 l of shots constituting the trajectory and a number Ns>1 of sampling points along each said shot;
• ii. determining, or receiving from a user input, a predetermined target sampling density;
• iii. determining, or receiving from a user input, a set of constraints including constraints on amplitudes of discrete time derivatives of the trajectory;
• iv. computing said trajectory by minimizing, subject to said set of constraints, a cost function defined by the difference between a first term, called attraction term, promoting adherence of the distribution of sampling points in k-space to said predetermined target sampling density, and a second term, called repulsion term, promoting separation in k-space between sampling points, said repulsion term being expressed as a sum of contributions corresponding to respective pairs of sampling points;
• wherein said trajectory (ST, MT) in k-space defines a Cartesian sampling of a central region(S) of the k-space.

A set of driving signals (DSG) for gradient coils of a magnetic resonance imaging scanner which, when applied to said gradient coils, drive them to generate time-varying magnetic field gradients (Gx, Gy, Gz) defining a trajectory (ST, MT) in k-space passing through a plurality of points (KS) called sampling points defining a pseudo-random sampling of the k-space, approximating a predetermined target sampling density;

• wherein said trajectory:
• is continuous and complies with a set of constraints including constraints on maximum amplitude and maximum slew rate of said time-varying magnetic field gradients;
• minimizes, subject to said set of constraints, a cost function defined by the difference between a first term, called attraction term, promoting adherence of the distribution of sampling points in k-space to said predetermined target sampling density, and a second term, called repulsion term, promoting separation in k-space between sampling points, said repulsion term being expressed as a sum of contributions corresponding to respective pairs of sampling points;
• wherein said trajectory (ST, MT) in k-space defines a Cartesian sampling of a central region(S) of the k-space.

A magnetic resonance imaging scanner comprising:

• a scanner bore (SB) inside which a body can be positioned;
• a primary coil (PC) configured to establish in the scanner bore a static and substantially uniform magnetic field (B0), called longitudinal field, oriented along a direction (z), called longitudinal direction;
• radio frequency coils (RFC) configured to transmit to said body at least one radio-frequency pulse (RFP) adapted for exciting nuclear spins inside said body and to acquire samples of a magnetic resonance signal emitted by the excited nuclear spin;
• gradient coils (GCx, GCy, GCz) configured to apply to said body time-varying magnetic field gradients (Gx, Gy, Gz) defining a trajectory (ST, MT) in k-space;
• a signal processing unit (SPU) to apply a nonlinear reconstruction algorithm to the acquired samples of the magnetic resonance signal for reconstructing a magnetic resonance image of said body;
• and
• a controller (CTR) configured to generate driving signals (DSR) for the radio frequency coils and (DSG) for the gradient coils;
• wherein the controller is configured to generate said driving signals for (DSG) for the gradient coils to generate a said time-varying magnetic field gradients (Gx, Gy, Gz) such that said a trajectory (ST) in k-space passes through a plurality of points (KS) called sampling points defining a pseudo-random sampling of the k-space, approximating a predetermined target sampling density, said trajectory being continuous and compliant with a set of constraints including constraints on maximum amplitude and maximum slew rate of said time-varying magnetic field gradients, said trajectory in k-space also minimizing, subject to said set of constraints, a cost function defined by the difference between a first term, called attraction term, promoting adherence of the distribution of sampling points in k-space to said predetermined target sampling density, and a second term, called repulsion term, promoting separation in k-space between sampling points, said repulsion term being expressed as a sum of contributions corresponding to respective pairs of sampling points;
• and wherein the controller is also configured to generate driving signals (DSR) for the radio frequency coils such that they acquire said samples of a magnetic resonance signal emitted by the excited nuclear spin in correspondence to the sampling points (KS) of the trajectory in k-space;
• wherein said trajectory (ST, MT) in k-space defines a Cartesian sampling of a central region (S) of the k-space.