MultiCoilMRI

class deepinv.physics.MultiCoilMRI(mask: Tensor | None = None, coil_maps: Tensor | int | None = None, img_size: tuple | None = (320, 320), three_d: bool = False, device=device(type='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).

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) – 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_parameters(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:: x (torch.Tensor) – image with shape [B,2,…,H,W].
Returns:: (torch.Tensor) multi-coil kspace measurements with shape [B,2,N,…,H,W] where N is coil dimension.

A_adjoint(y, mask=None, coil_maps=None, **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.
Returns:: (torch.Tensor) image with shape [B,2,…,H,W]

simulate_birdcage_csm(n_coils: int)[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)

update_parameters(mask: Tensor | None = None, coil_maps: Tensor | None = None, check_mask: bool = True, **kwargs)[source]

Update MRI subsampling mask and coil sensitivity maps.

Parameters:

mask (torch.nn.Parameter, torch.Tensor) – MRI mask
coil_maps (torch.nn.Parameter, torch.Tensor) – MRI coil sensitivity maps
check_mask (bool) – check mask dimensions before updating