SEMAC has shown great promise in obtaining distortion-free MR images near metallic implants. Nevertheless, the existing reconstruction procedure of SEMAC, which directly combines all resolved data elements with a complex sum, counteracts the SNR benefit brought by the long scan times associated with the additional z-phase encoding. To reclaim the SNR in the SEMAC-corrected images, we propose a new SEMAC reconstruction procedure that consists of SVD-based denoising and selective data inclusion.
Singular value decomposition (SVD) has been used for MR signal denoising in various applications, such as magnetic resonance spectroscopy [13
] and combining multi-echo data sets [14
]. The SVD-based denoising decomposes the resolved data into orthogonal components, followed by a low-rank approximation to keep those components that ideally correspond to signals. The SVD-based denoising of SEMAC multi-coil data removes the quadrature noise by retaining the signal component that corresponds to the largest singular value. By removing the quadrature noise, the resolved data elements containing useful signals can be more reliably differentiated from those only containing noise based on their magnitudes. This enables the selective data inclusion to exclude noise from the correction of through-plane distortions.
The key to the SVD-based denoising lies in determining the number of singular values preserved in the low-rank approximation. To uphold the rank-1 assumption of the SVD-based denoising, the extension of the proposed reconstruction procedure to accelerated SEMAC has to be carefully performed. Specifically, the parallel imaging reconstruction and the zero-filling partial Fourier reconstruction need to be performed prior to the denoising. By unfolding the aliasing in the phase encoding y
direction with the parallel imaging reconstruction, we ensure that each resolved data element does not contain the signals from other voxels subject to different coil sensitivities. On the other hand, the zero-filling partial Fourier reconstruction introduces blurring [8
], which causes the signal vector at one voxel to contain the data from its neighboring voxels. However, as coil sensitivities are smoothly varying (i.e., neighboring voxels' coil sensitivities are almost the same), the rank-1 assumption of the SVD-based denoising still holds; hence, the zero-filling induced blurring is acceptable for the denoising purpose.
There are different ways to combine the resolved data elements (e.g., the sum-of-squares combination and the complex-sum combination), which have different pros and cons in terms of implementation complexity, resultant SNR, and performance of artifact correction. The sum-of-squares is easy to implement, and results in a superior SNR than the linear complex sum. Even with the SVD denoising that completely removes quadrature noise, the linear complex sum still has higher noise level in the composite images, as shown with the experimental results. However, the sum-of-squares combination could be potentially problematic for the voxels that have large frequency dispersion, as the results in and show that the sum-of-squares combination can introduce undesirable intensity shading.
The linear complex-sum combination requires that the receiver and RF phase references in the SEMAC imaging sequence are carefully adjusted () such that the data resolved from multiple slices can be coherently summed up without taking the magnitude operation. The proposed SEMAC reconstruction procedure aims to significantly improve the SNR of the SEMAC-corrected images obtained using the complex-sum combination without compromising the correction of metal artifacts. The efficacy of the proposed technique has been demonstrated in the clinically important imaging scenarios where SEMAC-corrected images are liable to relatively low SNR. These scenarios include the incorporation of SEMAC with high readout bandwidth for less VAT-associated blurring, STIR for fat suppression, and accelerated acquisition for shorter scan times.