mrpro.operators.ConjugatePhaseFourierOp

class mrpro.operators.ConjugatePhaseFourierOp[source]

Bases: B0InformedFourierOp

Conjugate Phase (CP) B0-informed Fourier operator.

Performs an exact direct evaluation of the phase accumulation integral without separable approximation. Extremely computationally expensive.

References

[1]

Maeda A, Sano K, Yokoyama T. Reconstruction by two-dimensional time phase correction. IEEE Trans Med Imaging. 1988;7(1):26-31.

__init__(fourier_op: LinearOperator, b0_map: Tensor, readout_times: Tensor) → None[source]

Initialize B0-informed Fourier Operator.

Parameters:

• fourier_op (LinearOperator) – Underlying Fourier operator.

• b0_map (Tensor) – Off-resonance map in Hz. Shape (…, z, y, x).

• readout_times (Tensor) – Readout time vector in seconds. Shape (samples,).

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

property gram: LinearOperator[source]

Gram operator.

For a LinearOperator \(A\), the self-adjoint Gram operator is defined as \(A^H A\).

Note

This is the inherited default implementation.

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

Apply B0-informed Fourier transform to input tensor.

This transforms image data to k-space data, accounting for off-resonance effects.

Parameters:

x (Tensor) – Input image tensor with shape (…, coils, z, y, x).

Returns:

Transformed k-space tensor with shape (…, coils, k2, k1, k0).

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

Apply the adjoint of the B0-informed Fourier operator.

This transforms k-space data to image data, accounting for off-resonance effects.

Parameters:

y (Tensor) – Input k-space tensor with shape (…, coils, k2, k1, k0).

Returns:

Reconstructed image tensor in signal space with shape (…, coils, z, y, x).

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

Apply forward of B0InformedFourierOp.

Note

Prefer calling the instance of the operator as operator(x) over directly calling this method. See this PyTorch discussion.

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 | complex) → 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

__matmul__(other: LinearOperator) → LinearOperator[source]

__matmul__(other: Operator[Unpack[Tin2], tuple[Tensor]] | Operator[Unpack[Tin2], tuple[Tensor, ...]]) → Operator[Unpack[Tin2], 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 | complex) → 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)