MultiCoilMRI#

class deepinv.physics.MultiCoilMRI(mask=None, coil_maps=None, img_size=(320, 320), three_d=False, device=torch.device('cpu'), **kwargs)[source]#

Bases: MRIMixin, LinearPhysics

Multi-coil 2D or 3D MRI operator.

The linear operator operates in 2D slices or 3D volumes and is defined as:

\[y_n = \text{diag}(p) F \text{diag}(s_n) x\]

for \(n=1,\dots,N\) coils, where \(y_n\) are the measurements from the cth coil, \(\text{diag}(p)\) is the acceleration mask, \(F\) is the Fourier transform and \(\text{diag}(s_n)\) is the nth coil sensitivity.

The data x should be of shape (B,C,H,W) or (B,C,D,H,W) where C=2 is the channels (real and imaginary) and D is optional dimension for 3D MRI. Then, the resulting measurements y will be of shape (B,C,N,(D,)H,W) where N is the coils dimension.

Note

We provide various random mask generators (e.g. Cartesian undersampling) that can be used directly with this physics. See e.g. deepinv.physics.generator.mri.RandomMaskGenerator. If mask or coil maps are not passed, a mask and maps full of ones is used (i.e. no acceleration).

Note

You can also simulate basic birdcage coil sensitivity maps <https://mriquestions.com/birdcage-coil.html> by passing instead an integer to coil_maps using MultiCoilMRI(coil_maps=N, img_size=x.shape) (note this requires installing the sigpy library).

Note

This physics is directly compatible with FastMRI data using deepinv.datasets.FastMRISliceDataset. The dataset loads pairs of RSS images and multicoil kspace (x, y) where x = MultiCoilMRI().A_adjoint(y, rss=True, crop=True).

Parameters:

  • mask (torch.Tensor) – binary sampling mask which should have shape (H,W), (C,H,W), (B,C,H,W), or (B,C,…,H,W). If None, generate mask of ones with img_size.

  • coil_maps (torch.Tensor, str) – either Tensor, integer, or None. If complex valued (i.e. of complex dtype) coil sensitvity maps which should have shape (H,W), (N,H,W), (B,N,H,W) or (B,N,…,H,W). If None, generate flat coil maps of ones with img_size. If integer, simulate birdcage coil maps with integer number of coils (this requires sigpy installed).

  • img_size (tuple) – if mask or coil_maps not specified, flat mask or coil_maps of ones are created using img_size, where img_size can be of any shape specified above. If mask or coil_maps provided, img_size is ignored.

  • three_d (bool) – if True, calculate Fourier transform in 3D for 3D data (i.e. data of shape (B,C,D,H,W) where D is depth).

  • device (torch.device, str) – specify which device you want to use (i.e, cpu or gpu).

Examples:

Multi-coil MRI operator:

>>> from deepinv.physics import MultiCoilMRI
>>> seed = torch.manual_seed(0) # Random seed for reproducibility
>>> x = torch.randn(1, 2, 2, 2) # Define random 2x2 image B,C,H,W
>>> physics = MultiCoilMRI(img_size=x.shape) # Define coil map of ones
>>> physics(x).shape # B,C,N,H,W
torch.Size([1, 2, 1, 2, 2])
>>> coil_maps = torch.randn(1, 5, 2, 2, dtype=torch.complex64) # Define 5-coil sensitivity maps
>>> physics.update(coil_maps=coil_maps) # Update coil maps on the fly
>>> physics(x).shape
torch.Size([1, 2, 5, 2, 2])
A(x, mask=None, coil_maps=None, **kwargs)[source]#

Applies linear operator.

Optionally update MRI mask or coil sensitivity maps on the fly.

Parameters:
Returns:

(torch.Tensor) multi-coil kspace measurements with shape (B,2,N,...,H,W) where N is coil dimension.

Return type:

Tensor

A_adjoint(y, mask=None, coil_maps=None, rss=False, crop=False, **kwargs)[source]#

Applies adjoint linear operator.

Optionally update MRI mask or coil sensitivity maps on the fly.

Parameters:

  • y (torch.Tensor) – multi-coil kspace measurements with shape [B,2,N,…,H,W] where N is coil dimension.

  • mask (torch.Tensor) – optionally set the mask on-the-fly.

  • coil_maps (torch.Tensor) – optionally set the mask on-the-fly.

  • rss (bool) – perform root-sum-square reconstruction. This option is provided to match the original data of deepinv.datasets.FastMRISliceDataset, such that x = MultiCoilMRI().A_adjoint(y, rss=True).

  • crop (bool) – if True, crop last 2 dims of x to last 2 dims of img_size. This option is provided to match the original data of deepinv.datasets.FastMRISliceDataset, such that x = MultiCoilMRI().A_adjoint(y, crop=True).

Returns:

(torch.Tensor) image with shape (B,2,...,H,W) if not rss else (B,1,...,H,W)

Return type:

Tensor

A_dagger(y, mask=None, coil_maps=None, **kwargs)[source]#

Computes least squares solution to the MRI inverse problem, as proposed in SENSE: Sensitivity encoding for fast MRI.

By default uses conjugate gradient solver. Overwrite default solver arguments by passing kwargs. See deepinv.optim.utils.least_squares() for details.

The MRI mask or coil sensitivity maps are updated if passed as inputs to the function.

Parameters:
Returns:

(torch.Tensor) image with shape (B,2,...,H,W)

Return type:

Tensor

static estimate_coil_maps(y, calib_size=24, use_cupy=False)[source]#

Estimate coil sensitivity maps using ESPIRiT.

This was proposed in ESPIRiT — An Eigenvalue Approach to Autocalibrating Parallel MRI: Where SENSE meets GRAPPA.

Note this uses a suboptimal undifferentiable unbatched implementation provided by sigpy.

Optionally use cupy to accelerate on GPU, only if cupy is installed and a GPU is available.

Parameters:

  • y (torch.Tensor) – multi-coil kspace measurements with shape [B,2,N,…,H,W] where N is coil dimension.

  • calib_size (int) – optional square auto-calibration size in pixels, used by sigpy.

  • use_cupy (bool) – whether to attempt to use cupy for GPU acceleration.

Returns:

torch.Tensor of coil maps of complex dtype and shape [B,N,…,H,W]

Return type:

Tensor

noise(x, **kwargs)[source]#

Incorporates noise into the measurements \(\tilde{y} = N(y)\) and takes the mask into account.

Parameters:

  • x (torch.Tensor) – clean measurements

  • noise_level (None, float) – optional noise level parameter

Returns:

noisy measurements

Return type:

Tensor

simulate_birdcage_csm(n_coils)[source]#

Simulate birdcage coil sensitivity maps. Requires library sigpy.

Parameters:

n_coils (int) – number of coils N

Return torch.Tensor:

coil maps of complex dtype of shape (N,H,W)

Return type:

Tensor

update_parameters(mask=None, coil_maps=None, check_mask=True, **kwargs)[source]#

Update MRI subsampling mask and coil sensitivity maps.

Parameters:

Examples using MultiCoilMRI:#

Tour of MRI functionality in DeepInverse

Tour of MRI functionality in DeepInverse