Complex Data

• For single channel data [1]– Real and imag. images are normally distributed with N(S, σ2)– Then magnitude images follow Rice dist., which is

approximately normal in “high” SNR (3+)• ≈N(sqrt(S2+ σ2), σ2)

• For multi-channel data and parallel acceleration [2]:– Optimal SNR recon (w/ coil sensitivities, SENSE): complex

images are normal, magnitude images are Rice (Rayleigh noise)– Sum-of-squares magnitude images: magnitude images have

non-central Χ-dist. noise

[1] Gudbjartsson and Patz. The Rician Distribution of Noisy MRI Data. [2] Dietrich. MRM 2008.

CRLB with Complex Data

• In previous designs, the algorithm was allowed to optimize σi

2 for each magnitude image with Σσi2 =

constant– For the complex data case, the real and imag. images are

assumed to have same noise level– Thus the situation is essentially the same, where we choose

σi2 for each series

– Further, the results should be comparable to previous ones with magnitude images• Due to the relations in noise variance between complex and

magnitude images, i.e. for reasonable SNR, the variances are all about the same

B0 Robustness

• Previously, a question about how finely to sample the off-resonance phase for the design

• This is plotted with 100 points• I use 64 points in the analysis– Now takes 2+ days to solve all the problems up to 16

total images

Optimal Design• The Li paper used a criterion as σ/θ2, a greater scaling than CoV

citing [3]– Still need go through that to understand why that’s a logical/better choice

• “Alphabetic” optimality of Fisher information matrix– A-optimality – minimize the mean of CRLBs, tr(F-1)– D-optimality – minimize the determinant, |F-1|– E-optimality – maximize the smallest eigenvalue of F

• Previously you may remember we looked at the SVD of J for mcDESPOT

– G-optimality – minimize the maximum variance of a parameter– We’re doing a weighted combination (by 1/θ) version of A

• Often times these variants have the same optimal design– They each have different properties and perhaps some are easier to solve,

need to read more

[3] Atkinson, Donev, and Tobias. Optimal Experimental Designs.

Complex PCVFA On-Res.: Protocol

Complex PCVFA On-Res.: T1

Complex PCVFA On-Res.: T2

Complex PCVFA vs. Magn. PCVFA

Complex, B0 Robust w/o B0 Map: Protocol

Complex, B0 Robust w/o B0 Map: T1

Complex, B0 Robust w/o B0 Map: T2

Complex, B0 Robust w/ B0 Map: Protocol

Complex, B0 Robust w/ B0 Map: T1

Complex, B0 Robust w/ B0 Map: T2

Complex, B0 Robust w/ B0 Map: B0

Thoughts

• Is complex data worth pursuing?– Definitely a big improvement over magn. only,

which seemed terrible– But is it improved enough?

• Should evaluate DESPOT2-FM for comparison– I might expect it to not do that great as I had

tough time with it for mouse data– Other study data had much less severe B0

inhomogeneity