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Two-point search (Triay Bagur et al. 2019)
Reminder:
Frequencies in 1000 runs with same signal different noise.
Fitting model:
Initial: ρw = 1, ρf = 0
Initial: ρw = 0, ρf = 1
Fat fraction:
R2* = 0
True FF = 0.7
R2* = 300
True FF = 0.7
The generated signal will have S(0) = 1.
However, the real data will have varing S(0) values.
The signals behave the same way after scalling.
Simulating the noisy data with SNR of 70[1].
Fitting a single signal
Signals for TE = every 0.1ms between 0 and 10ms.
Signals for TE = [1.15, 2.3, 3.45, 4.6, 5.75, 6.9] ms
SSD objective:
Initial ρw = 1, ρf = 0
Initial ρw = 0, ρf = 1
Local miminum:
simulated noisy signal
Magnitude
fitted signal
Magnitude
Constants chosen for the simulated data:
ρw = 0.3, ρf = 0.7, r = [0.087, 0.694, 0.128, 0.004, 0.039, 0.048], freq = [-0.498, -0.447, -0.345, -0.261, -0.063, 0.064] kHz
Doing two point search for the phantom data:
256x256x20x6
(from the single peak model)
FF map
R2* map
(by Euler's Formula)
The signal for voxel (80, 145) at layer 12
Cross section of the phantom data at layer 12,
across different TEs
(Single Peak Model)
(because )
This representation of |S|^2 makes it clear that the signal magnitude function|S| is symmetric in the fat/ water density parameters.
Ambiguity Doesn't always occur when there are multiple peaks.
Fitting subject data (320, 320, 40, 6)
Subject data at layer 20
Fat fraction map
R2* map
(no attenuation)
(attenuation)
Further tasks:
Known Parameters
The SSD for different R2* and Fat fraction pairs with ground truth R2* = 300, FF=0.7
3d plot here
Distribution of the magnitude of noise
Bray et al. (2018)