mrpro.operators.models.SaturationRecovery

class mrpro.operators.models.SaturationRecovery[source]

Bases: SignalModel[Tensor, Tensor]

Signal model for saturation recovery.

__init__(saturation_time: float | Tensor | Sequence[float]) → None[source]

Initialize saturation recovery signal model for T1 mapping.

Parameters:

saturation_time (float | Tensor | Sequence[float]) – delay between saturation and acquisition. Shape (time, ...).

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

Apply the saturation recovery signal model.

Calculates the signal based on the formula: \(S(t_{sat}) = M_0 (1 - e^{-t_{sat} / T_1})\), where t_{sat} are the saturation times.

Parameters:

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

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

Returns:

Signal calculated for each saturation time. Shape (times ...), for example (times, *other, coils, z, y, x), or (times, samples) where times is the number of saturation times.

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

Apply forward of SaturationRecovery.

Note

Prefer calling the instance of the SaturationRecovery 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)