MRI

class deepinv.physics.MRI(mask: Tensor | None = None, img_size: tuple | None = (320, 320), three_d: bool = False, device='cpu', **kwargs)

Bases: MRIMixin, DecomposablePhysics

Single-coil accelerated 2D or 3D magnetic resonance imaging.

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

\[y = MFx\]

where \(M\) applies a mask (subsampling operator), and \(F\) is the 2D or 3D discrete Fourier Transform. This operator has a simple singular value decomposition, so it inherits the structure of deepinv.physics.DecomposablePhysics() and thus have a fast pseudo-inverse and prox operators.

The complex images \(x\) and measurements \(y\) should be of size (B, C,…, H, W) with C=2, where the first channel corresponds to the real part and the second channel corresponds to the imaginary part. The ... is an optional depth dimension for 3D MRI data.

A fixed mask can be set at initialisation, or a new mask can be set either at forward (using physics(x, mask=mask)) or using update_parameters.

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 is not passed, a mask full of ones is used (i.e. no acceleration).

Parameters:

• mask (torch.Tensor) – binary mask, where 1s represent sampling locations, and 0s otherwise. The mask size can either be (H,W), (C,H,W), (B,C,H,W), (B,C,…,H,W) where H, W are the image height and width, C is channels (which should be 2) and B is batch size.

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

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Examples:

Single-coil accelerated MRI operator with subsampling mask:

>>> from deepinv.physics import MRI
>>> seed = torch.manual_seed(0) # Random seed for reproducibility
>>> x = torch.randn(1, 2, 2, 2) # Define random 2x2 image
>>> mask = 1 - torch.eye(2) # Define subsampling mask
>>> physics = MRI(mask=mask) # Define mask at initialisation
>>> physics(x)
tensor([[[[ 0.0000, -1.4290],
          [ 0.4564, -0.0000]],

         [[ 0.0000,  1.8622],
          [ 0.0603, -0.0000]]]])
>>> physics = MRI(img_size=x.shape) # No subsampling
>>> physics(x)
tensor([[[[ 2.2908, -1.4290],
          [ 0.4564, -0.1814]],

         [[ 0.3744,  1.8622],
          [ 0.0603, -0.6209]]]])
>>> physics.update_parameters(mask=mask) # Update mask on the fly
>>> physics(x)
tensor([[[[ 0.0000, -1.4290],
          [ 0.4564, -0.0000]],

         [[ 0.0000,  1.8622],
          [ 0.0603, -0.0000]]]])

update_parameters(mask: Tensor | None = None, check_mask: bool = True, **kwargs)

Update MRI subsampling mask.

Parameters:

• mask (torch.nn.Parameter, torch.Tensor) – MRI mask

• check_mask (bool) – check mask dimensions before updating

Examples using MRI:

A tour of forward sensing operators

A tour of forward sensing operators

Self-supervised MRI reconstruction with Artifact2Artifact

Self-supervised MRI reconstruction with Artifact2Artifact

Self-supervised learning with Equivariant Imaging for MRI.

Self-supervised learning with Equivariant Imaging for MRI.