mrpro.operators.models.SpoiledGRE

class mrpro.operators.models.SpoiledGRE[source]

Bases: SignalModel[Tensor, Tensor, Tensor]

Spoiled gradient echo signal model.

__init__(flip_angle: float | Tensor, echo_time: float | Tensor, repetition_time: float | Tensor) → None[source]

Initialize spoiled gradient echo signal model.

Assumes perfect spoiling and a longitudinal steady state. This is a simplified special case of TransientSteadyStateWithPreparation.

The model is defined as: \(S = M_0 e^{-t_r / T_2^*} \frac{\sin(\alpha)(1 - e^{-t_e / T_1})}{(1 - \cos(\alpha) e^{-t_e / T_1})}\)

where \(M_0\) is the equilibrium magnetization, \(\alpha\) is the flip angle, \(t_e\) is the echo time, and \(t_r\) is the repetition time.

Parameters:

• flip_angle (float | Tensor) – Flip angle in radians.

• echo_time (float | Tensor) – Echo time.

• repetition_time (float | Tensor) – Repetition time.

__call__(m0: Tensor, t1: Tensor, t2star: Tensor) → tuple[Tensor][source]

Calculate the Spoiled Gradient Echo signal.

Parameters:

• m0 (Tensor) – Equilibrium signal / proton density. Shape (...), for example (*other, coils, z, y, x) or (samples).

• t1 (Tensor) – Longitudinal (T1) relaxation time. Shape (...), for example (*other, coils, z, y, x) or (samples).

• t2star (Tensor) – Effective transverse (T2*) relaxation time. Shape (...), for example (*other, coils, z, y, x) or (samples).

Returns:

Signal Shape (1 ...), for example (1, *other, coils, z, y, x) or (1, samples).

forward(m0: Tensor, t1: Tensor, t2star: Tensor) → tuple[Tensor][source]

Apply forward of SpoiledGRE.

Note

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

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

__add__(other: Tensor | complex) → 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], tuple[Tensor, ...]]) → 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 | complex) → 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)