create_fast_chauffert_density

mrinufft.trajectories.sampling.create_fast_chauffert_density(shape, wavelet_basis, nb_wavelet_scales)

Create a density based on an approximated Chauffert method.

This implementation is based on this tutorial: philouc/mri_acq_recon_tutorial. It is a fast approximation of the proposition from [CCW13], where a sampling density is derived from compressed sensing equations to maximize guarantees of exact image recovery for a specified sparse wavelet domain decomposition.

In this approximation, the decomposition dimensions are considered independent and computed separately to accelerate the density generation.

Parameters:

• shape (tuple[int, ...]) – The shape of the density grid.

• wavelet_basis (str, pywt.Wavelet) – The wavelet basis to use for wavelet decomposition, either as a built-in wavelet name from the PyWavelets package or as a custom pywt.Wavelet object.

• nb_wavelet_scales (int) – The number of wavelet scales to use in decomposition.

Returns:

A density array created using a faster approximation based on 1D projections of the wavelet transform.

Return type:

NDArray

See also

pywt.wavelist

A list of wavelet decompositions available in the PyWavelets package used inside the function.

pywt.Wavelet

A wavelet object accepted to generate Chauffert densities.

References

[CCW13]

Chauffert, Nicolas, Philippe Ciuciu, and Pierre Weiss. “Variable density compressed sensing in MRI. Theoretical vs heuristic sampling strategies.” In 2013 IEEE 10th International Symposium on Biomedical Imaging, pp. 298-301. IEEE, 2013.