mrinufft.trajectories

Collection of trajectories and tools used for non-Cartesian MRI.

See also the trajectories examples: Trajectories Examples

Functions

R2D	Initialize 2D rotation matrix.
Ra	Initialize 3D rotation matrix around an arbitrary vector.
Rv	Initialize 3D rotation matrix from two vectors.
Rx	Initialize 3D rotation matrix around x axis.
Ry	Initialize 3D rotation matrix around y axis.
Rz	Initialize 3D rotation matrix around z axis.
get_closest_fibonacci_number	Provide the closest Fibonacci number.
initialize_2D_cones	Initialize a 2D cone trajectory.
initialize_2D_eccentric	Initialize a 2D ECCENTRIC trajectory.
initialize_2D_fibonacci_spiral	Initialize a 2D Fibonacci spiral trajectory.
initialize_2D_lissajous	Initialize a 2D Lissajous trajectory.
initialize_2D_polar_lissajous	Initialize a 2D polar Lissajous trajectory.
initialize_2D_propeller	Initialize a 2D PROPELLER trajectory, as proposed in [Pip99].
initialize_2D_radial	Initialize a 2D radial trajectory.
initialize_2D_random_walk	Initialize a 2D random walk trajectory.
initialize_2D_rings	Initialize a 2D ring trajectory, as proposed in [HHN08].
initialize_2D_rosette	Initialize a 2D rosette trajectory.
initialize_2D_sinusoide	Initialize a 2D sinusoide trajectory.
initialize_2D_spiral	Initialize a 2D algebraic spiral trajectory.
initialize_2D_travelling_salesman	Initialize a 2D trajectory using a Travelling Salesman Problem (TSP)-based path.
initialize_2D_vds_spiral	Initialize a 2D variable density spiral (VDS) trajectory.
initialize_2D_waves	Initialize a 2D waves trajectory.
initialize_3D_annular_shells	Initialize 3D trajectories with annular shells.
initialize_3D_cones	Initialize 3D trajectories with cones.
initialize_3D_eccentric	Initialize a 3D ECCENTRIC trajectory.
initialize_3D_floret	Initialize 3D trajectories with FLORET.
initialize_3D_golden_means_radial	Initialize 3D radial trajectories with golden means-based structure.
initialize_3D_helical_shells	Initialize 3D trajectories with helical shells.
initialize_3D_park_radial	Initialize 3D radial trajectories with a spiral structure.
initialize_3D_phyllotaxis_radial	Initialize 3D radial trajectories with phyllotactic structure.
initialize_3D_random_walk	Initialize a 3D random walk trajectory.
initialize_3D_repi	Initialize 3D REPI trajectory.
initialize_3D_seiffert_shells	Initialize 3D trajectories with Seiffert shells.
initialize_3D_seiffert_spiral	Initialize 3D trajectories with modulated Seiffert spirals.
initialize_3D_travelling_salesman	Initialize a 3D trajectory using a Travelling Salesman Problem (TSP)-based path.
initialize_3D_turbine	Initialize 3D TURBINE trajectory.
initialize_3D_wave_caipi	Initialize 3D trajectories with Wave-CAIPI.
initialize_3D_wong_radial	Initialize 3D radial trajectories with a spiral structure.
conify	Distort 2D or 3D trajectories into cones along the \(k_z\)-axis.
duplicate_along_axes	Duplicate a trajectory along the specified axes.
epify	Create multi-readout shots from trajectory composed of single-readouts.
get_grappa_caipi_positions	Generate a Cartesian k-space sampling mask for GRAPPA with optional CAIPI shifts.
get_packing_spacing_positions	Generate a k-space positions for a fixed spacing and packing.
get_random_loc_1d	Get slice index at a random position.
oversample	Resample a trajectory to increase the number of samples using interpolation.
precess	Rotate trajectories as a precession around the \(k_z\)-axis.
prewind	Add pre-winding/positioning to the trajectory.
radialize_center	Radialize a trajectory.
rewind	Add rewinding to the trajectory.
rotate	Rotate 2D or 3D trajectories over the different axes.
shellify	Stack 2D or 3D trajectories over the \(k_z\)-axis to make a sphere.
stack	Stack 2D or 3D trajectories over the \(k_z\)-axis.
stack_random	Stack a 2D trajectory with random location.
stack_spherically	Stack 2D or 3D trajectories over the \(k_z\)-axis to make a sphere.
unepify	Recover single-readout shots from multi-readout trajectory.
check_hardware_constraints	Check if a trajectory satisfies the gradient hardware constraints.
compute_gradients_and_slew_rates	Compute the gradients and slew rates from a normalized trajectory.
connect_gradient	Get the gradient connections for a set of start and end points.
convert_gradients_to_slew_rates	Derive the gradients over time to provide slew rates.
convert_gradients_to_trajectory	Integrate gradients over time to provide a normalized trajectory.
convert_slew_rates_to_gradients	Integrate slew rates over time to provide gradients.
convert_trajectory_to_gradients	Derive a normalized trajectory over time to provide gradients.
create_chauffert_density	Create a density based on Chauffert's method.
create_cutoff_decay_density	Create a density with central plateau and polynomial decay.
create_energy_density	Create a density based on energy in the Fourier spectrum.
create_fast_chauffert_density	Create a density based on an approximated Chauffert method.
create_polynomial_density	Create a density with polynomial decay from the center.
get_prephasors_and_spoilers	Get the prephasors and spoiler gradients for a trajectory.
initialize_algebraic_spiral	Initialize the algebraic spiral type.
initialize_shape_norm	Initialize the norm for a given shape.
initialize_tilt	Initialize the tilt angle.
min_length_connection	Get the minimum length of gradient connection for a trajectory.
normalize_trajectory	Normalize an un-normalized/natural trajectory for NUFFT use.
parameterize_by_arc_length	Adjust the trajectory to have a uniform distribution over the arc-length.
patch_center_anomaly	Re-position samples to avoid center anomalies.
project_trajectory	Projects the trajectory onto hardware constraint set.
sample_from_density	Sample points based on a given density distribution.
unnormalize_trajectory	Un-normalize a NUFFT-normalized trajectory.

Classes

Acquisition	Acquisition configuration for MRI sequences.
FloatEnum	An Enum for float that is case insensitive for ist attributes.
Gammas	Enumerate gyromagnetic ratios for common nuclei in MR.
GradientLinearProjection	Implements the gradient of F(q1, q2) given by Eq 11 in_[Proj].
GroupL2SoftThresholding	Group L2 Soft Thresholding (Shrinkage) Operator.
Hardware	Hardware configuration for MRI sequences.
NormShapes	Enumerate shape norms.
Packings	Enumerate available packing method for shots.
SiemensGradient	Common hardware configurations for Siemens MRI systems.
Spirals	Enumerate algebraic spiral types.
StrEnum	An Enum for str that is case insensitive for its attributes.
Tilts	Enumerate available tilts.
VDSorder	Available ordering for variable density sampling.
VDSpdf	Available law for variable density sampling.