Examples

Executed when the documentation is built: every figure and number comes from the code on the page. Each page has an Open in Colab button, so you need nothing but a browser to run it. The ideas behind them are in Explanations, and every function they call is in API reference.

Course

Eleven lessons from a k-space tensor to a learned reconstruction, read in order (Course).

Lesson	Contents
1. Your data as tensors	Tensors in BART’s layout; BART commands on tensors
2. From k-space to an image	Undersampled Cartesian reconstruction, step by step
3. Coil sensitivities	Coil sensitivity estimation and its effect on the reconstruction
4. Joint reconstruction of image and sensitivity maps	Joint estimation of image and coil sensitivities from a small calibration region
5. Choosing a regularizer	Tikhonov, wavelet and total-variation regularization; regularization weight
6. Custom encoding and solver	Encoding operator and solver, identical to pics
7. Basics of non-Cartesian imaging	Trajectories, NUFFT, density compensation, point spread function
8. Radial SENSE	Golden-angle radial SENSE
9. Nonlinear inversion for T2 mapping	Model-based \(T_2\) mapping from raw data
10. Plug-and-play reconstruction	Plug-and-play with a pretrained denoiser
11. Training an unrolled network	Unrolled network trained through ADMM

Tours

Standalone examples beyond the Course. Each names the lessons it assumes (Tours).

Tour	Contents
Readout oversampling and apodization	Readout oversampling removal; Fermi and Hann apodization
EPI Nyquist ghost and ramp sampling	EPI Nyquist ghost correction; ramp-sampling regridding
Receive bias field	Receive bias field estimation with N4
Gradient nonlinearity	Gradient nonlinearity correction from spherical-harmonic coefficients
Off-resonance correction of spiral imaging	Spiral off-resonance deblurring: multifrequency interpolation, time-segmented reconstruction
Rigid head motion from navigators	Rigid head motion from orthogonal navigator planes
Susceptibility distortion in EPI	EPI susceptibility distortion correction from reversed phase encoding
Noise prewhitening	Noise prewhitening and SNR
Dynamic golden-angle radial MRI	Dynamic golden-angle radial reconstruction with temporal total variation
Subspace-constrained T1 mapping	Subspace \(T_1\) mapping from a continuous inversion-recovery scan
Parameter maps from scanner images	\(T_2\) mapping from DICOM magnitude images
Networks for complex volumes	Networks for complex multi-contrast volumes; patchwise execution
Staged training of an unrolled network	Staged training of unrolled networks
Training without a reference	Self-supervised training from undersampled data
Annealed plug-and-play	Plug-and-play with an annealed noise level
Uncertainty estimation	Calibrated voxel-wise uncertainty

Requirements

The scripts need a built bartorch, brainweb-dl, which downloads the BrainWeb phantoms several examples build their images from, and matplotlib and cmap for the figures:

pip install bartorch brainweb-dl matplotlib cmap

The learned-regularization lessons and tours additionally require lightning, torchio, monai and deepinv, and the corrections tours PyHySCO; the Course and Tours pages name what each needs.