By Santiago Aja-Fernández, Gonzalo Vegas-Sánchez-Ferrero
This certain textual content provides a finished evaluation of tools for modeling sign and noise in magnetic resonance imaging (MRI), offering a scientific learn, classifying and evaluating the varied and sundry estimation and filtering concepts. gains: presents a whole framework for the modeling and research of noise in MRI, contemplating assorted modalities and acquisition thoughts; describes noise and sign estimation for MRI from a statistical sign processing viewpoint; surveys the various tips on how to eliminate noise in MRI acquisitions from a pragmatic standpoint; experiences diversified ideas for estimating noise from MRI info in unmarried- and multiple-coil structures for absolutely sampled acquisitions; examines the difficulty of noise estimation whilst speeded up acquisitions are thought of, and parallel imaging equipment are used to reconstruct the sign; contains appendices protecting likelihood density services, mixtures of random variables used to derive estimators, and invaluable MRI datasets.
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Extra info for Statistical Analysis of Noise in MRI: Modeling, Filtering and Estimation
36) σl2 = |Ω| Kl with |Ω| the final number of pixels in the FOV. Note the final noise power is greater than in the fully sampled case due to the reduced k-space averaging, as it will be the case with SENSE. On the contrary, the iDFT may be computed after zero-padding the missing (not sampled) k-space lines, and then the noise in each coil of the x-space will be Gaussian with variance : σl2 = 1 σ2 . 4 Statistical Models for pMRI Acquisitions 43 In the latter case, the noise power is reduced with respect to the fully sampled case, since we average exactly the same number of samples but only 1 of each r of them contributes a noise sample (this will also be the case with GRAPPA).
To reconstruct a single value, an interpolation of the pixels in a neighborhood around the missing value is considered. That neighborhood is extended to all the coils. In the example shown in the figure, the reconstructed value at position (k x , k y ) for the first coil is reconstructed as 4 1 s1R (k x , k y ) = slS (k x − m, k y − n)ωl1 (m, n). 5 Accelerated Acquisitions: Parallel Imaging 27 Fig. 17 Auto Calibration signal lines: the center of the k-space is fully sampled in order to estimate the reconstruction weights in GRAPPA where ωl1 (m, n) is a set of 4 reconstruction kernels defined to interpolate data from all the coils into the fist one.
5 we show a multiple-coil array used of head imaging acquisition. The presence of various signals at the same time makes the global pipeline slightly different to the single-coil one. The basic block diagram is surveyed in Fig. 6. Let us assume a system with L RF-coils. The acquired signal in coil l = 1, 2, . . 9) V where Cl (r) is the spatial sensitivity of coil l at r. We can rewrite this equation as sl (k) = Cl (x)S(x)e j2πk·x dx = V Sl (x)e j2πk·x dx. 4 Multiple-Coil Acquisition Process 17 Fig.