SequentialMRI

class deepinv.physics.SequentialMRI(mask: Tensor | None = None, img_size: tuple | None = (320, 320), device='cpu', **kwargs)[source]

Bases: DynamicMRI

Single-coil accelerated magnetic resonance imaging using sequential sampling.

Let \(S\) be a subsampling mask with given acceleration. \(S_t\) is a time-varying mask with the sequential sampling pattern e.g. non-overlapping lines or spokes, such that \(S=\bigcup_t S_t\). The sequential MRI operator then simulates a time sequence of k-space samples:

\[y_t = S_t F x\]

where \(F\) is the 2D discrete Fourier Transform, the image \(x\) is of shape (B, 2, H, W) and measurements \(y\) is of shape (B, 2, T, H, W) where the first channel corresponds to the real part and the second channel corresponds to the imaginary part.

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.

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

Parameters:

  • mask (torch.Tensor) – binary mask \(S_t,t=1\ldots T\), where 1s represent sampling locations, and 0s otherwise. The mask size can either be (H,W), (T,H,W), (C,T,H,W) or (B,C,T,H,W) where H, W are the image height and width, T is time-steps, C is channels (typically 2) and B is batch size.

  • img_size (tuple) – if mask not specified, blank 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.

  • device (torch.device) – cpu or gpu.

Examples:

Single-coil accelerated sequential MRI operator:

>>> from deepinv.physics import SequentialMRI
>>> x = torch.randn(1, 2, 2, 2) # Define random image of shape (B,C,H,W)
>>> mask = torch.zeros(1, 2, 3, 2, 2) # Empty demo time-varying mask with 3 frames
>>> physics = SequentialMRI(mask=mask) # Physics with given mask
>>> physics.update_parameters(mask=mask) # Alternatively set mask on-the-fly
>>> physics(x).shape # MRI sequential samples
torch.Size([1, 2, 3, 2, 2])
A(x: Tensor, mask: Tensor | None = None, **kwargs) → Tensor[source]

Applies the forward operator \(y = A(x)\).

If a mask/singular values is provided, it is used to apply the forward operator, and also stored as the current mask/singular values.

Parameters:

  • x (torch.Tensor) – input tensor

  • mask (torch.nn.Parameter, float) – singular values.

Returns:

(torch.Tensor) output tensor

A_adjoint(y: Tensor, mask: Tensor | None = None, keep_time_dim=False, **kwargs) → Tensor[source]

Computes the adjoint of the forward operator \(\tilde{x} = A^{\top}y\).

Parameters:

  • y (torch.Tensor) – input tensor

  • mask (torch.nn.Parameter, float) – input mask

  • keep_time_dim (bool) – if True, adjoint is calculated frame-by-frame. Used for visualisation. If False, flatten the time dimension before calculating.

Returns:

(torch.Tensor) output tensor

Examples using SequentialMRI:

Self-supervised MRI reconstruction with Artifact2Artifact

Self-supervised MRI reconstruction with Artifact2Artifact