mrpro.operators.models.WASABI

class mrpro.operators.models.WASABI[source]

Bases: SignalModel[Tensor, Tensor, Tensor, Tensor]

WASABI signal model.

__init__(offsets: Tensor | Sequence[float] | float, rf_duration: float | Tensor = 0.005, b1_nominal: float | Tensor = 3.70e-6, gamma: float = GYROMAGNETIC_RATIO_PROTON) → None[source]

Initialize WASABI signal model for mapping of B0 and B1 [SCHU2016].

This model uses a slight modification from the original published model. The parameter a corresponds to d/c in the original model.

Parameters:

  • offsets (Tensor | Sequence[float] | float) – frequency offsets [Hz] with shape (offsets, ...)

  • rf_duration (float | Tensor, default: 0.005) – RF pulse duration [s]

  • b1_nominal (float | Tensor, default: 3.70e-6) – nominal B1 amplitude [T]

  • gamma (float, default: GYROMAGNETIC_RATIO_PROTON) – gyromagnetic ratio [Hz/T]

References

[SCHU2016]

Schuenke P, Zaiss M (2016) Simultaneous mapping of water shift and B1(WASABI)—Application to field-Inhomogeneity correction of CEST MRI data. MRM 77(2). https://doi.org/10.1002/mrm.26133

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

Apply the forward operator.

For more information, see forward.

Note

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

forward(b0_shift: Tensor, relative_b1: Tensor, c: Tensor, a: Tensor) → tuple[Tensor][source]

Apply the WASABI (Water Shift and B1) signal model.

Parameters:

  • b0_shift (Tensor) – B0 field in homogeneity or off-resonance shift in Hz. Shape , for example *other, coils, z, y, x or samples.

  • relative_b1 (Tensor) – Relative B1 amplitude scaling factor (actual B1 / nominal B1). Shape , for example *other, coils, z, y, x or samples.

  • c (Tensor) – Signal amplitude parameter (related to M0). Shape , for example *other, coils, z, y, x or samples.

  • a (Tensor) – Signal modulation scaling parameter, corresponds to d/c in the original model. Shape , for example *other, coils, z, y, x or samples.

Returns:

Signal calculated for each frequency offset. Shape offsets .... For example offsets, *other, coils, z, y, x, or offsets, samples where offsets is the number of frequency offsets.

__add__(other: Operator[Unpack[Tin], Tout]) → Operator[Unpack[Tin], Tout][source]
__add__(other: Tensor) → Operator[Unpack[Tin], tuple[Unpack[Tin]]]

Operator addition.

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

__matmul__(other: Operator[Unpack[Tin2], tuple[Unpack[Tin]]]) → Operator[Unpack[Tin2], Tout][source]

Operator composition.

Returns lambda x: self(other(x))

__mul__(other: Tensor | complex) → Operator[Unpack[Tin], Tout][source]

Operator multiplication with tensor.

Returns lambda x: self(x*other)

__radd__(other: Tensor) → Operator[Unpack[Tin], tuple[Unpack[Tin]]][source]

Operator right addition.

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

__rmul__(other: Tensor | complex) → Operator[Unpack[Tin], Tout][source]

Operator multiplication with tensor.

Returns lambda x: other*self(x)