1 / 16

Complex Data

Complex Data. For single channel data [1] Real and imag . images are normally distributed with N(S, σ 2 ) Then magnitude images follow Rice dist., which is approximately normal in “high” SNR (3+) ≈N( sqrt (S 2 + σ 2 ), σ 2 ) For multi-channel data and parallel acceleration [2]:

ramona
Download Presentation

Complex Data

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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.

  2. CRLB with Complex Data • In previous designs, the algorithm was allowed to optimize σi2 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

  3. 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

  4. 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.

  5. Complex PCVFA On-Res.: Protocol

  6. Complex PCVFA On-Res.: T1

  7. Complex PCVFA On-Res.: T2

  8. Complex PCVFA vs. Magn. PCVFA

  9. Complex, B0 Robust w/o B0 Map: Protocol

  10. Complex, B0 Robust w/o B0 Map: T1

  11. Complex, B0 Robust w/o B0 Map: T2

  12. Complex, B0 Robust w/ B0 Map: Protocol

  13. Complex, B0 Robust w/ B0 Map: T1

  14. Complex, B0 Robust w/ B0 Map: T2

  15. Complex, B0 Robust w/ B0 Map: B0

  16. 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

More Related