DynamicMRI

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

Bases: MRI, TimeMixin

Single-coil accelerated dynamic magnetic resonance imaging.

The linear operator operates in 2D+t videos and is defined as

\[y_t = M_t Fx_t\]

where \(M_t\) applies a time-varying mask, and \(F\) is the 2D 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, 2, T, H, W) where the first channel corresponds to the real part and the second channel corresponds to the imaginary part.

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, 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, 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.

• device (torch.device) – cpu or gpu.

---

Examples:

Single-coil accelerated 2D+t MRI operator:

>>> from deepinv.physics import DynamicMRI
>>> seed = torch.manual_seed(0) # Random seed for reproducibility
>>> x = torch.randn(1, 2, 2, 2, 2) # Define random video of shape (B,C,T,H,W)
>>> mask = torch.rand_like(x) > 0.75 # Define random 4x subsampling mask
>>> physics = DynamicMRI(mask=mask) # Physics with given mask
>>> physics.update_parameters(mask=mask) # Alternatively set mask on-the-fly
>>> physics(x)
tensor([[[[[-0.0000,  0.7969],
           [-0.0000, -0.0000]],

          [[-0.0000, -1.9860],
           [-0.0000, -0.4453]]],


         [[[ 0.0000,  0.0000],
           [-0.8137, -0.0000]],

          [[-0.0000, -0.0000],
           [-0.0000,  1.1135]]]]])

A(x: Tensor, mask: Tensor | None = None, **kwargs) → Tensor

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, **kwargs) → Tensor

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

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

Parameters:

• y (torch.Tensor) – input tensor

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

Returns:

(torch.Tensor) output tensor

A_dagger(y: Tensor, mask: Tensor | None = None, **kwargs) → Tensor

Computes \(A^{\dagger}y = x\) in an efficient manner leveraging the singular vector decomposition.

Parameters:

y (torch.Tensor) – a measurement \(y\) to reconstruct via the pseudoinverse.

Returns:

(torch.Tensor) The reconstructed image \(x\).

check_mask(mask: Tensor | None = None, **kwargs) → None

Updates MRI mask and verifies mask shape to be B,C,T,H,W.

:param torch.nn.Parameter, float MRI subsampling mask.

noise(x, **kwargs)

Incorporates noise into the measurements \(\tilde{y} = N(y)\)

Parameters:

x (torch.Tensor) – clean measurements

Return torch.Tensor:

noisy measurements

to_static(mask: Tensor | None = None) → MRI

Convert dynamic MRI to static MRI by removing time dimension.

Parameters:

mask (torch.Tensor) – new static MRI mask. If None, existing mask is flattened (summed) along the time dimension.

Return MRI:

static MRI physics

Examples using DynamicMRI:

Self-supervised MRI reconstruction with Artifact2Artifact

Self-supervised MRI reconstruction with Artifact2Artifact