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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]: – 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.

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CRLB with Complex Data In previous designs, the algorithm was allowed to optimize σ i 2 for each magnitude image with Σσ i 2 = 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 σ i 2 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

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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

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Optimal Design The Li paper used a criterion as σ/θ 2, a greater scaling than CoV citing [3] – Still need go through that to understand why thats 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 – Were 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.

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Complex PCVFA On-Res.: Protocol

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Complex PCVFA On-Res.: T1

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Complex PCVFA On-Res.: T2

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Complex PCVFA vs. Magn. PCVFA

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Complex, B0 Robust w/o B0 Map: Protocol

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Complex, B0 Robust w/o B0 Map: T1

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Complex, B0 Robust w/o B0 Map: T2

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DESPOT2: Precision Over Tissue Space This shows the precision over many tissues, i.e. how good the protocol is for tissues it is not optimized for.

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Complex, B0 Robust w/ B0 Map: Protocol

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Complex, B0 Robust w/ B0 Map: T1

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Complex, B0 Robust w/ B0 Map: T2

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Complex, B0 Robust w/ B0 Map: B0

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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

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Optimal Experimental Design Theory. Motivation To better understand the existing theory and learn from tools that exist out there in other fields To further.

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