| CPC G01R 33/4822 (2013.01) [G01R 33/385 (2013.01); G01R 33/543 (2013.01); G01R 33/5616 (2013.01)] | 15 Claims |

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1. A method of performing magnetic resonance imaging of a body using a magnetic resonance imaging scanner comprising a scanner bore (SB), a primary coil (PC), radio frequency coils (RFC), gradient coils (GCx, GCy, GCz) and a signal-processing unit (SPU), the method comprising the steps of:
a. positioning the body (BD) in a scanner bore (SB) where a static and substantially uniform magnetic field (B0), called longitudinal field, oriented along a direction (z), called longitudinal direction, is established by the primary coil (PC);
b. using all or part of the radio-frequency coils (RFC) to transmit to said body at least one radio-frequency pulse (RFP) adapted to excite nuclear spins inside said body;
c. after said or each said radio-frequency pulse, using the gradient coils (GCx, GCy, GCz) to apply to said body a time-varying magnetic field gradient (Gx, Gy, Gz) defining a trajectory (ST) in k-space and simultaneously using all or part of the radio-frequency coils to acquire samples of a magnetic resonance signal emitted by the excited nuclear spin, each sample corresponding to a point (KS) of the k-space belonging to said trajectory; and
d. using the signal processing unit (SPU) to apply a nonlinear reconstruction algorithm to the acquired samples to reconstruct a magnetic resonance image of said body;
wherein said trajectory (ST, MT) in k-space is a continuous trajectory complying with a set of constraints including constraints on maximum amplitude and maximum slew rate of said time-varying magnetic field gradient, such that the points (KS) of the k-space corresponding to the samples, called sampling points, define a pseudo-random sampling of the k-space, matching a predetermined target sampling density, said trajectory in k-space minimizing, subject to said set of constraints, a cost function defined by the difference between a first term, called attraction term, promoting consistency of the distribution of sampling points in k-space with 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 each said contribution is weighted by a weight which increase with temporal separation of the sampling points along said trajectory in k-space.
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