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A subspace approach to blind coil sensitivity estimation in parallel MRI

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In parallel MRI, subsampled k-space data are simultaneously collected by multiple coils... Since pointwise-multiplication in image domain corresponds to convolution in k-space, parallel MRI problem can be expressed as a blind image deconvolution problem; consequently, a subspace approach can be used to estimate the k-space coefficients of the CSMs. If yi, x and hi represent fully sampled k-space data, true image, and k-space coefficients of the iCSM, then the problem can be written as yi = x*hi = Xhi... Thus, if x has full rank, then the -space of Y is equivalent to the -space of H... As a result, the -space (equivalently row-space) vectors used to reconstruct yi from subsampled data in PRUNO, can be used for the estimation of k-space coefficients of CSMs efficiently using the following optimization problem: h = argmaxh //Vh//+μ//Rh//, where R represents a low-pass filter, and V involves convolution matrices of filters obtained from rowspace vectors... A Gaussian function was selected for the low-pass R... The eigenvector associated with the largest eigenvalue of VV+μ RR was calculated to yield the 8 × 8 estimated k-space coefficients of the CSMs for μ = 5... Estimated CSM for one coil and its SoS-normalized version are demonstrated in Figure 1... SENSE reconstructions for one of the frames are given in Figure 2 for the estimated CSMs and their SoS-normalized versions... As seen, inhomogeneity and artifacts existing in SENSE reconstruction is significantly reduced with the normalized CSMs. Compared to the image domain processing, the proposed k-space estimation of CSM was 10 times faster... The proposed k-space approach for CSM estimation using subspace methods and a simple normalization provides both low computational complexity and the flexibility to incorporate both regularization and a low-dimensional parameterization of the smooth CSMs.

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SENSE reconstructions from the estimated sensitivities on the left and their SoS normalized versions on the right. Red arrow points to a strong artifact.
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Figure 2: SENSE reconstructions from the estimated sensitivities on the left and their SoS normalized versions on the right. Red arrow points to a strong artifact.

Mentions: Estimated CSM for one coil and its SoS-normalized version are demonstrated in Figure 1. SENSE[4] reconstructions for one of the frames are given in Figure 2 for the estimated CSMs and their SoS-normalized versions. As seen, inhomogeneity and artifacts existing in SENSE reconstruction is significantly reduced with the normalized CSMs. Compared to the image domain processing, the proposed k-space estimation of CSM was 10 times faster.


A subspace approach to blind coil sensitivity estimation in parallel MRI
SENSE reconstructions from the estimated sensitivities on the left and their SoS normalized versions on the right. Red arrow points to a strong artifact.
© Copyright Policy - open-access
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4043905&req=5

Figure 2: SENSE reconstructions from the estimated sensitivities on the left and their SoS normalized versions on the right. Red arrow points to a strong artifact.
Mentions: Estimated CSM for one coil and its SoS-normalized version are demonstrated in Figure 1. SENSE[4] reconstructions for one of the frames are given in Figure 2 for the estimated CSMs and their SoS-normalized versions. As seen, inhomogeneity and artifacts existing in SENSE reconstruction is significantly reduced with the normalized CSMs. Compared to the image domain processing, the proposed k-space estimation of CSM was 10 times faster.

View Article: PubMed Central - HTML

AUTOMATICALLY GENERATED EXCERPT
Please rate it.

In parallel MRI, subsampled k-space data are simultaneously collected by multiple coils... Since pointwise-multiplication in image domain corresponds to convolution in k-space, parallel MRI problem can be expressed as a blind image deconvolution problem; consequently, a subspace approach can be used to estimate the k-space coefficients of the CSMs. If yi, x and hi represent fully sampled k-space data, true image, and k-space coefficients of the iCSM, then the problem can be written as yi = x*hi = Xhi... Thus, if x has full rank, then the -space of Y is equivalent to the -space of H... As a result, the -space (equivalently row-space) vectors used to reconstruct yi from subsampled data in PRUNO, can be used for the estimation of k-space coefficients of CSMs efficiently using the following optimization problem: h = argmaxh //Vh//+μ//Rh//, where R represents a low-pass filter, and V involves convolution matrices of filters obtained from rowspace vectors... A Gaussian function was selected for the low-pass R... The eigenvector associated with the largest eigenvalue of VV+μ RR was calculated to yield the 8 × 8 estimated k-space coefficients of the CSMs for μ = 5... Estimated CSM for one coil and its SoS-normalized version are demonstrated in Figure 1... SENSE reconstructions for one of the frames are given in Figure 2 for the estimated CSMs and their SoS-normalized versions... As seen, inhomogeneity and artifacts existing in SENSE reconstruction is significantly reduced with the normalized CSMs. Compared to the image domain processing, the proposed k-space estimation of CSM was 10 times faster... The proposed k-space approach for CSM estimation using subspace methods and a simple normalization provides both low computational complexity and the flexibility to incorporate both regularization and a low-dimensional parameterization of the smooth CSMs.

No MeSH data available.