mrpro.operators.FourierOp

class mrpro.operators.FourierOp[source]

Bases: LinearOperator

Fourier Operator class.

This is the recommended operator for all Fourier transformations. It auto-detects if a non-uniform or regular fast Fourier transformation is required. For Cartesian data on a regular grid, the data is sorted and a FFT is used. For non-Cartesian data, a NUFFT with regridding is used. It also includes padding/cropping to the reconstruction matrix size.

The operator can directly be constructed from a KData object to match its trajectory and header information, see FourierOp.from_kdata.

__init__(recon_matrix: SpatialDimension[int], encoding_matrix: SpatialDimension[int], traj: KTrajectory) → None[source]

Initialize Fourier Operator.

Parameters:

• recon_matrix (SpatialDimension[int]) – dimension of the reconstructed image

• encoding_matrix (SpatialDimension[int]) – dimension of the encoded k-space

• traj (KTrajectory) – the k-space trajectories where the frequencies are sampled

classmethod from_kdata(kdata: KData, recon_shape: SpatialDimension[int] | None = None) → Self[source]

Create an instance of FourierOp from kdata with default settings.

Parameters:

• kdata (KData) – k-space data

• recon_shape (Optional[SpatialDimension[int]], default: None) – Dimension of the reconstructed image. Defaults to KData.header.recon_matrix.

property gram: LinearOperator[source]

Return the gram operator.

property H: LinearOperator[source]

Adjoint operator.

Obtains the adjoint of an instance of this operator as an AdjointLinearOperator, which itself is a an LinearOperator that can be applied to tensors.

Note: linear_operator.H.H == linear_operator

__call__(*args: Unpack) → Tout[source]

Apply the forward operator.

For more information, see forward.

Note

Prefer using operator_instance(*parameters), i.e. using __call__ over using forward.

adjoint(x: Tensor) → tuple[Tensor][source]

Adjoint operator mapping the coil k-space data to the coil images.

Parameters:

x (Tensor) – coil k-space data with shape: (... coils k2 k1 k0)

Returns:

coil image data with shape: (... coils z y x)

forward(x: Tensor) → tuple[Tensor][source]

Forward operator mapping the coil-images to the coil k-space data.

Parameters:

x (Tensor) – coil image data with shape: (... coils z y x)

Returns:

coil k-space data with shape: (... coils k2 k1 k0)

operator_norm(initial_value: Tensor, dim: Sequence[int] | None, max_iterations: int = 20, relative_tolerance: float = 1e-4, absolute_tolerance: float = 1e-5, callback: Callable[[Tensor], None] | None = None) → Tensor[source]

Power iteration for computing the operator norm of the operator.

Parameters:

• initial_value (Tensor) – initial value to start the iteration; must be element of the domain. if the initial value contains a zero-vector for one of the considered problems, the function throws an ValueError.

• dim (Sequence[int] | None) –

  The dimensions of the tensors on which the operator operates. The choice of dim determines how the operator norm is inperpreted. For example, for a matrix-vector multiplication with a batched matrix tensor of shape (batch1, batch2, row, column) and a batched input tensor of shape (batch1, batch2, row):

  • If dim=None, the operator is considered as a block diagonal matrix with batch1*batch2 blocks and the result is a tensor containing a single norm value (shape (1, 1, 1)).

  • If dim=(-1), batch1*batch2 matrices are considered, and for each a separate operator norm is computed.

  • If dim=(-2,-1), batch1 matrices with batch2 blocks are considered, and for each matrix a separate operator norm is computed.

  Thus, the choice of dim determines implicitly determines the domain of the operator.

• max_iterations (int, default: 20) – maximum number of iterations

• relative_tolerance (float, default: 1e-4) – absolute tolerance for the change of the operator-norm at each iteration; if set to zero, the maximal number of iterations is the only stopping criterion used to stop the power iteration.

• absolute_tolerance (float, default: 1e-5) – absolute tolerance for the change of the operator-norm at each iteration; if set to zero, the maximal number of iterations is the only stopping criterion used to stop the power iteration.

• callback (Callable[[Tensor], None] | None, default: None) – user-provided function to be called at each iteration

Returns:

An estimaton of the operator norm. Shape corresponds to the shape of the input tensor initial_value with the dimensions specified in dim reduced to a single value. The pointwise multiplication of initial_value with the result of the operator norm will always be well-defined.

__add__(other: LinearOperator | Tensor) → LinearOperator[source]

__add__(other: Operator[Tensor, tuple[Tensor]]) → Operator[Tensor, tuple[Tensor]]

Operator addition.

Returns lambda x: self(x) + other(x) if other is a operator, lambda x: self(x) + other if other is a tensor

__and__(other: LinearOperator) → LinearOperatorMatrix[source]

Vertical stacking of two LinearOperators.

A&B is a LinearOperatorMatrix with two rows, with (A&B)(x) == (A(x), B(x)). See mrpro.operators.LinearOperatorMatrix for more information.

__matmul__(other: LinearOperator) → LinearOperator[source]

__matmul__(other: Operator[Unpack, tuple[Tensor]]) → Operator[Unpack, tuple[Tensor]]

Operator composition.

Returns lambda x: self(other(x))

__mul__(other: Tensor | complex) → LinearOperator[source]

Operator elementwise left multiplication with tensor/scalar.

Returns lambda x: self(x*other)

__or__(other: LinearOperator) → LinearOperatorMatrix[source]

Horizontal stacking of two LinearOperators.

A|B is a LinearOperatorMatrix with two columns, with (A|B)(x1,x2) == A(x1)+B(x2). See mrpro.operators.LinearOperatorMatrix for more information.

__radd__(other: Tensor) → LinearOperator[source]

Operator addition.

Returns lambda x: self(x) + other*x

__rmul__(other: Tensor | complex) → LinearOperator[source]

Operator elementwise right multiplication with tensor/scalar.

Returns lambda x: other*self(x)