Method and apparatus for accelerated magnetic resonance imaging

1. A method of performing magnetic resonance imaging of a body comprising the steps of:

a) immerging the body (BD) in a static and substantially uniform magnetic field (BO), called longitudinal field oriented along a direction (z), called longitudinal direction;

b) transmitting to said body a plurality of radio-frequency pulse (RFP) adapted for exciting nuclear spins inside said body;

c) after each said radio-frequency pulse, applying to said body a time-varying magnetic field gradient (G x , G y ) defining a respective non-parametric trajectory (ST) in a k-space and simultaneously acquiring samples of a magnetic resonance signal emitted by the excited nuclear spin, each sample corresponding to a point (K i , KS) of the k-space belonging to said trajectory, wherein the points of the k-space corresponding to the samples define a pseudo-random sampling of the k-space, following a predetermined sampling density; and

d) applying a sparsity-promoting nonlinear reconstruction algorithm to the acquired samples for reconstructing a magnetic resonance image of said body, said image being formed by a two-dimensional, three-dimensional or four-dimensional array of pixels;

the number of non-parametric trajectories in the k-space, each following a respective radio-frequency pulse, along which said samples are acquired, being lower than the number of pixels or voxels along one direction of said array;

wherein

a number of samples along each of said trajectories exceeds a number of pixels along at least one dimension of said array; and in that:

at least in a central region of the k-space, the distance (Δk) between any two adjacent points belonging to a same trajectory is lower than 1/FOV, FOV being a size of a field of view of the reconstructed image of the object.

2. The method of claim 1 , wherein step c further comprises determining the points of the k-space belonging to said or each trajectory by projecting a predetermined sampling density distribution onto a set of discrete pushforward measures.

3. The method of claim 2 , wherein said set of discrete pushforward measures is constituted by the pushforward measures defined on all continuous trajectories in the k-space corresponding to time-varying magnetic field gradients whose maximum amplitude and maximum slew rate do not exceed respective limits.

4. The method of claim 1 , wherein said step d) comprises reconstructing a magnetic resonance image of said body by optimizing a nonlinear sparsity-promoting criterion, function of the acquired samples, said optimizing being performed using a Fast Iterative Soft Thresholding Algorithm.

5. The method of claim 1 , performed using a magnetic resonance imaging apparatus, wherein, during step c), said applying to said body a time-varying magnetic field gradient (G x , G y ) defining a non-parametric trajectory (ST) in a k-space is carried out using a minimum gradient raster time for said magnetic resonance imaging apparatus.

6. A magnetic resonance imaging apparatus comprising:

a first coil (LC) suitable for generating a static magnetic field (B0), called longitudinal field, substantially uniform within a volume of interest and oriented along a direction, called longitudinal direction;

a set of gradient coils (CGx, CGy, CGz) suitable for generating, within said volume of interest, a time-varying magnetic field gradient;

at least one radio-frequency coils (TC) suitable for generating a radio-frequency pulse within said volume of interest; and

a control unit (CU) configured or programmed to drive said gradient coils and said radio-frequency coil or coils, and to acquire and process signals received by said radio-frequency coil or coils, to carry out a method according to claim 1 .