Jung-Hsiang Chang^{1}, Yi-Hsun Yang^{1}, Tzu-Cheng Chao^{2,3}, and Cheng-Wen Ko^{1}

Compressed Sensing can be very useful in accelerating Phase-encoded Proton MRSI. The sampling functions and the reconstruction settings have been known as critical factors in recovering the data of the accelerated acquisition. The present work compared the choices of sampling functions and the regularization information in the reconstruction in a hope to optimize the framework of Compressed Sensing based MRSI. The results suggest that the spectral quality can be retained for as high as five-fold acceleration with an appropriate undersampling and reconstruction setting.

A volunteer data was acquired on a 3.0T scanner (GE Discovery MR750, Waukesha, WI) using an 8 channel head coil with TR = 1.5s, TE = 30ms, FOV = 22 cm, Matrix Size = 24x24 and 20mm slice thickness. A pseudo-random sampling function with a centrally weighted variable density distribution ^{5,6} on the k-space was used to subsample the data at the acceleration of 2, 3, and 5 respectively. In addition to using any random sampling pattern, a series of subsampling masks were generated for the designated acceleration factors. The mask featuring the point spread function (PSF) with highest main peak to side lobe ratio in the image domain of the given acceleration was selected for the simulated undersampling. In the reconstruction, Fourier transformation was firstly performed along the time domain. Subsequently the k-space of each frequency was reconstructed with Compressed Sensing algorithm:

$$\min_{\rho}|s-E\rho|_2+\lambda_1|Ψ\rho|_1+\lambda_2|TV \rho|_1$$

where ρ is the MRSI, s : the k-space signal, E : the 2D Fourier Transformation operator, $$$Ψ$$$ : the sparsity transformation and TV : the total variation operator. The following experiments also compare three different reconstruction settings: (1) $$$Ψ$$$ is a Daubechies Wavelet transformation with λ_{1}=0.005, λ_{2}=0.002; (2) $$$Ψ$$$ is an identity matrix with λ_{1}=0.005, λ_{2}=0.002; (3) $$$Ψ$$$ is an identity matrix with λ_{1}=0.005, λ_{2}=0. The images were reconstructed with non-linear conjugate gradient algorithm. The reconstruction generally converges after 60 iterations. Each coil data was reconstructed separately then combined for the analysis by the LCModel.^{7}

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Figure 1. The original spectral data overlay on a T2W
image. The two voxels indicated by the red boxes are chosen for analysis in the
following comparisons.

Figure 2. The spectral data from the voxel of parenchyma
were reconstructed with different choices of PSF and acceleration settings.
Smoothing effect are noticed in the accelerated reconstruction while the noise
levels are slightly decreased.

Figure 3. The spectral data from the voxel of parenchyma were reconstructed
with different choices of PSF and acceleration settings. Significant spectrum
aliasing can be found as the accelration factor increases. Lower aliasing
artifacts can be found with optimizing PSF.

Figure 4. These plots are the spectral data of the parenchyma voxel
reconstructed with three different regularization schemes at three-fold
acceleration. The reconstruction using wavelet transformation and total
variation gives the highest SNR. When the sparse transformation is removed, the
SNR becomes lower with higher fitting uncertainty. The entire spectrum is
distorted when the total variation is further excluded.