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Section Navigation

  • mrinufft.operators
    • operators.autodiff
      • DeepInvPhyNufft
      • MRINufftAutoGrad
    • operators.base
      • check_backend
      • get_operator
      • list_backends
      • power_method
      • FourierOperatorBase
      • FourierOperatorCPU
      • FourierOperatorSimple
    • operators.cartesian
      • MRICartesianOperator
      • RawMRICartesianOperator
    • operators.interfaces
      • interfaces.bart
        • MRIBartNUFFT
        • RawBartNUFFT
      • interfaces.cufinufft
        • MRICufiNUFFT
        • RawCufinufftPlan
      • interfaces.ducc0
        • MRIDUCC0
        • RawDUCC0
      • interfaces.finufft
        • MRIfinufft
        • RawFinufftPlan
      • interfaces.gpunufft
        • make_pinned_smaps
        • MRIGpuNUFFT
        • RawGpuNUFFT
      • interfaces.nfft
        • MRInfft
        • RawPyNFFT3
      • interfaces.nudft_numpy
        • get_fourier_matrix
        • get_implicit_matrix
        • implicit_type1_ndft
        • implicit_type2_ndft
        • MRInumpy
        • RawNDFT
      • interfaces.pynufft_cpu
        • MRIPynufft
        • RawPyNUFFT
      • interfaces.sigpy
        • MRISigpyNUFFT
        • RawSigpyNUFFT
      • interfaces.tfnufft
        • MRITensorflowNUFFT
      • interfaces.torchkbnufft
        • MRITorchKbNufft
        • TorchKbNUFFTcpu
        • TorchKbNUFFTgpu
      • interfaces.utils
        • utils.gpu_utils
    • operators.off_resonance
      • MRIFourierCorrected
    • operators.stacked
      • stacked2traj3d
      • traj3d2stacked
      • MRIStackedNUFFT
      • MRIStackedNUFFTGPU
    • operators.subspace
      • MRISubspace
  • mrinufft.trajectories
    • trajectories.display
      • display.advanced
        • get_gridded_trajectory
      • display.config
        • displayConfig
      • display.gradients
        • display_gradients
        • display_gradients_simply
      • display.trajectories
        • display_2D_trajectory
        • display_3D_trajectory
    • trajectories.display3D
    • trajectories.gradients
      • connect_gradient
      • get_prephasors_and_spoilers
      • min_length_connection
      • patch_center_anomaly
      • preprocess
      • solve_trivial
    • trajectories.inits
      • inits.cones
        • initialize_2D_cones
        • initialize_3D_cones
      • inits.eccentric
        • initialize_2D_eccentric
        • initialize_3D_eccentric
      • inits.floret
        • initialize_3D_floret
      • inits.fmri
        • initialize_3D_repi
        • initialize_3D_turbine
      • inits.lissajous
        • initialize_2D_lissajous
        • initialize_2D_polar_lissajous
      • inits.propeller
        • initialize_2D_propeller
      • inits.radial
        • initialize_2D_radial
        • initialize_3D_golden_means_radial
        • initialize_3D_park_radial
        • initialize_3D_phyllotaxis_radial
        • initialize_3D_wong_radial
      • inits.random_walk
        • initialize_2D_random_walk
        • initialize_3D_random_walk
      • inits.rings
        • initialize_2D_rings
      • inits.rosette
        • initialize_2D_rosette
      • inits.seiffert
        • initialize_3D_seiffert_shells
        • initialize_3D_seiffert_spiral
      • inits.shells
        • initialize_3D_annular_shells
        • initialize_3D_helical_shells
      • inits.spiral
        • initialize_2D_fibonacci_spiral
        • initialize_2D_spiral
        • initialize_2D_vds_spiral
      • inits.travelling_salesman
        • initialize_2D_travelling_salesman
        • initialize_3D_travelling_salesman
      • inits.wave_caipi
        • initialize_3D_wave_caipi
      • inits.waves
        • initialize_2D_sinusoide
        • initialize_2D_waves
    • trajectories.maths
      • maths.fibonacci
        • generate_fibonacci_circle
        • generate_fibonacci_lattice
        • generate_fibonacci_sphere
        • get_closest_fibonacci_number
        • is_from_fibonacci_sequence
      • maths.primes
        • compute_coprime_factors
      • maths.rotations
        • R2D
        • Ra
        • Rv
        • Rx
        • Ry
        • Rz
      • maths.tsp_solver
        • solve_tsp_with_2opt
    • trajectories.projection
      • linear_projection
      • parameterize_by_arc_length
      • project_trajectory
      • GradientLinearProjection
      • GroupL2SoftThresholding
    • trajectories.sampling
      • create_chauffert_density
      • create_cutoff_decay_density
      • create_energy_density
      • create_fast_chauffert_density
      • create_polynomial_density
      • sample_from_density
    • trajectories.tools
      • tools.caipi
        • get_grappa_caipi_positions
        • get_packing_spacing_positions
      • tools.epi
        • epify
        • unepify
      • tools.functional
        • shellify
        • stack_spherically
      • tools.random
        • get_random_loc_1d
        • stack_random
      • tools.transforms
        • conify
        • duplicate_along_axes
        • oversample
        • precess
        • radialize_center
        • rotate
        • stack
      • tools.winding
        • prewind
        • rewind
    • trajectories.trajectory2D
    • trajectories.trajectory3D
    • trajectories.utils
      • check_hardware_constraints
      • compute_gradients_and_slew_rates
      • convert_gradients_to_slew_rates
      • convert_gradients_to_trajectory
      • convert_slew_rates_to_gradients
      • convert_trajectory_to_gradients
      • initialize_algebraic_spiral
      • initialize_shape_norm
      • initialize_tilt
      • normalize_trajectory
      • unnormalize_trajectory
      • Acquisition
      • CaseInsensitiveEnumMeta
      • FloatEnum
      • Gammas
      • Hardware
      • NormShapes
      • Packings
      • SI
      • SIEMENS
      • Spirals
      • StrEnum
      • Tilts
      • VDSorder
      • VDSpdf
  • mrinufft.density
    • density.geometry_based
      • cell_count
      • voronoi
      • voronoi_unique
    • density.nufft_based
      • pipe
    • density.utils
      • flat_traj
      • normalize_weights
  • mrinufft.io
    • io.cfl
      • cfl2traj
      • traj2cfl
    • io.nsp
      • read_arbgrad_rawdat
      • read_trajectory
      • write_gradients
      • write_trajectory
    • io.pulseq
      • acq2opts
      • pulseq_gre
      • read_pulseq_traj
    • io.siemens
      • read_siemens_rawdat
    • io.utils
      • add_phase_to_kspace_with_shifts
      • nifti_affine
      • remove_extra_kspace_samples
      • siemens_quat_to_rot_mat
  • mrinufft.extras
    • extras.cartesian
      • fft
      • ifft
    • extras.data
      • fse_simulation
      • get_brainweb_map
    • extras.field_map
      • compute_mfi_coefficients
      • compute_mti_coefficients
      • compute_svd_coefficients
      • get_complex_fieldmap_rad
      • make_b0map
      • make_t2smap
      • C_lazy
    • extras.optim
      • cg
      • loss_l2_AHreg
      • loss_l2_reg
      • lsmr
      • lsqr
      • scaled_dcp
    • extras.smaps
      • cartesian_espirit
      • coil_compression
      • espirit
      • low_frequency
  • mrinufft._utils
    • check_error
    • proper_trajectory
    • sizeof_fmt
    • MethodRegister
  • mrinufft._array_compat
    • auto_cast
    • get_array_module
    • is_cuda_array
    • is_cuda_tensor
    • is_host_array
    • pin_memory
    • with_numpy
    • with_numpy_cupy
    • with_tensorflow
    • with_torch
  • API
  • trajectories.inits

inits.rings#

Ring trajectory initialization.

Functions

initialize_2D_rings

Initialize a 2D ring trajectory, as proposed in [HHN08].

previous

initialize_3D_random_walk

next

initialize_2D_rings

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