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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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Left: estimated coil sensitivity for one of 12 coils; Right: estimate normalized by the sum-of-squares of the estimated sensitivities.
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Figure 1: Left: estimated coil sensitivity for one of 12 coils; Right: estimate normalized by the sum-of-squares of the estimated sensitivities.

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
Left: estimated coil sensitivity for one of 12 coils; Right: estimate normalized by the sum-of-squares of the estimated sensitivities.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 1: Left: estimated coil sensitivity for one of 12 coils; Right: estimate normalized by the sum-of-squares of the estimated sensitivities.
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.