LookupTable

class blochsim.estimators.LookupTable

Bases: Estimator

Read one unknown back from a monotonic signal curve.

Linear interpolation between the two nearest atoms of a one-parameter model removes the dictionary grid spacing from the estimate. The classic use is the MP2RAGE T1 map [1].

Parameters:

• acquisition (Simulator, default=None) – The sequence being inverted, with every property that is neither unknown nor measured separately already fixed. Omit to give signals to fit().

• combine (callable, default=None) – Reduces (..., contrasts) signals to the (...) values the curve is in, for example the MP2RAGE unified image. Not needed for a single-contrast model.

• monotonic (bool, default=True) – Keep only the longest monotonic run of the curve.

Notes

Signals outside span are read as the nearer endpoint. The lookup runs where the signals are and is not streamed.

References

[1]

Marques, J. P., Kober, T., Krueger, G., van der Zwaag, W., Van de Moortele, P.-F., Gruetter, R., “MP2RAGE, a self bias-field corrected sequence for improved segmentation and T1-mapping at high field”, NeuroImage 49.2 (2010), pp. 1271-1281. https://doi.org/10.1016/j.neuroimage.2009.10.002

Examples

import torch
from blochsim.estimators import LookupTable
from blochsim.simulators import MP2RAGESimulator

protocol = dict(
    TI=(800.0, 2700.0), flip=(4.0, 5.0),
    TRspgr=6.7, TRmp2rage=6000.0, nshots=128,
)
T1 = torch.arange(50.0, 5000.0, 50.0)
blocks = MP2RAGESimulator(**protocol).simulate(
    T1=T1, inv_efficiency=0.96
)
unified = (blocks[:, 0] * blocks[:, 1]) / blocks.square().sum(-1)

table = LookupTable().fit(signals=unified[:, None], parameters=T1[:, None])
print(table.points, "points spanning", [round(v, 3) for v in table.span])
print(table(torch.tensor([[0.1], [-0.2]])).flatten().tolist())

75 points spanning [-0.5, 0.49]
[1086.536376953125, 1721.1234130859375]

Methods

fit	Fit the estimator over a sampling of the tissue it will meet.
from_coefficients	Map coefficients already in this estimator's basis.
map	Estimate the tissue parameters of a measured volume.
training_set	Simulate a training set from the properties given to fit().
uncertainty_of	Uncertainty of each map, as a standard deviation in the map's units.

property fitted

Whether the table holds a curve.

property points

Number of points in the table.

property span

Signal range (low, high) covered by the table.