MRI#

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

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).

Note

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

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.

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]]]])

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

Adjoint operator.

Optionally perform crop and magnitude to match FastMRI data.

By default, crop and magnitude are not performed. By setting mag=crop=True, the outputs will be consistent with deepinv.datasets.FastMRISliceDataset.

Parameters:

y (torch.Tensor) – input kspace of shape (B,C,…,H,W)
mask (torch.Tensor) – optionally set mask on-the-fly.
mag (bool) – perform complex magnitude. This option is provided to match the original data of deepinv.datasets.FastMRISliceDataset, such that x = MRI().A_adjoint(y, mag=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 = MRI().A_adjoint(y, crop=True).

V(x)[source]#

Applies the \(V\) operator of the SVD decomposition.

Note

This method should be overwritten by the user to define its custom DecomposablePhysics operator.

Parameters:: x (torch.Tensor) – input tensor

V_adjoint(x)[source]#

Applies the \(V^{\top}\) operator of the SVD decomposition.

Note

This method should be overwritten by the user to define its custom DecomposablePhysics operator.

Parameters:: x (torch.Tensor) – input tensor

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

Update MRI subsampling mask.

Parameters:

mask (torch.nn.parameter.Parameter, torch.Tensor) – MRI mask
check_mask (bool) – check mask dimensions before updating

Examples using `MRI`:#

A tour of forward sensing operators

Tour of MRI functionality in DeepInverse

Self-supervised MRI reconstruction with Artifact2Artifact

Self-supervised learning with Equivariant Imaging for MRI.

MRI#

Examples using MRI:#

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Examples using `MRI`:#