Variable Rates Undersampling Scheme for Fast brain T1ρ mapping
Yuanyuan Liu1, Yanjie Zhu1, Jing Cheng1, Xin Liu1, and Dong Liang1,2

1Paul C. Lauterbur Research Center for Biomedical Imaging, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China, 2Research center for Medical AI, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China


T mapping requires several T-weighted images with different spin lock times to obtain the T maps, resulting in a long scan time.Compressed sensing has shown good performance in fast quantitative T mapping. In this work, we developed a variable acceleration rates undersampling strategy to reduce the scan time. A signal compensation with low-rank plus sparse model was used to reconstruct the T-weighted images. Specifically, a feature descriptor was used to pick up useful features from the residual images. Preliminary results show that the proposed method achieves a 5.76-fold acceleration and obtain more accurate T maps than the existing methods.


Compressed sensing (CS) based reconstruction methods have been successfully applied in quantitative T mapping1-4 to reduce the scan time. According to the CS theory, the noise like aliasing artifacts from undersampling can be removed using the minimum $$$\ell_1$$$-norm. We previously developed a signal compensation strategy based low-rank plus sparse matrix method (SCOPE)5 for fast T mapping and achieved a 5-fold acceleration. In T mapping,soft tissues with short T, i.e. scalp and subcutaneous fat, show high signal intensities in short TSL images. These signal would generate strong aliasing artifacts after undersampling, which are difficult to remove since its signal intensity level is much higher than noise level. Therefore, images with short TSLs are prone to have aliasing artifacts in reconstruction,especially at a high acceleration rate. Regularizations are helpful for aliasing artifacts suppression but bring in smoothing artifacts4.

To alleviate this issue, we propose a variable rates undersampling strategy to improve the reconstruction accuracy at high acceleration factors. Keeping net acceleration factor constant, the acceleration factor for each T-weighted image increases while the fully sampled percentage in k-space center decreases with increasing TSL. That is, short TSL images mainly provide signal intensity and contrast information, and long TSL images contribute to fine structure reservation. To further improve the reconstruction performance, a modified soft-thresholding combined with feature descriptors was used in reconstruction iterations.


Figure 1a shows the proposed variable rates undersampling scheme in the ky-TSL space for a net acceleration factor R=3.19.The phase encoding lines for each T-weighted image are randomly sampled according to variable density undersampling scheme.

The SCOPE5 method was used for image reconstruction with the model as follows:

$$min{||L||_*}+\lambda||S||_1 \ \ \ \ s.t.\ \ C(X)=L+S,E(X)=d\ \ \ \ \ \ \ \ [1]$$

where$$$||L||_*$$$ is the nuclear norm of the low-rank matrix L; $$$||S||_1$$$is the $$$\ell_1$$$-norm of the sparse matrix S; X is the image series; λ is a regularization parameter; d is the undersampled k-space data; C(∙) performs pixel-wise signal compensation; E is the encoding operator 7,8.

To solve the above equation, an initial compensation coefficient is calculated using the T map estimated from the fully sampled central k-space. Iterative hard thresholding of the singular values for L and a modified soft-thresholding of the entries for S are used to solve the optimization problem in Eq. [1]. A new T map is estimated from the reconstructed images and then used to update the compensation coefficient. The reconstruction and signal compensation coefficient updating steps are repeated alternately until convergence.

The formula for the modified soft-thresholding is:

$$Feat(m)=\frac{m}{|m|}max(0,|m|-\mu(m))\ \ \ \ \ \ \ \ \ \ [2]$$

$$\mu(m)=(1-Feat(m))*(1-r)*\delta+r*\delta \ \ \ \ \ \ \ \ \ [3]$$

where m is the element of image matrix, $$$Feat(\cdot) $$$ represents the feature descriptor, which picks up useful features from residual image between reconstructed images of consecutive iterations6.The element in $$$Feat(\cdot)$$$ is in the interval [0, 1],representing the probability of belonging to the feature part; δ is the global threshold and r is the adjustable ratio. Both parameters are empirically chosen.


All MR data were acquired on a 3T scanner (Trio, SIEMENS, Germany) using a twelve-channel head coil. 3 healthy volunteers ( male, age 25±2) were recruited (IRB proved, written informed consent obtained). Each volunteer was scanned using a spin-lock embedded turbo spin-echo (TSE) sequence9. Imaging parameters were: TR/TE=4000ms/9ms, spin-lock frequency 500 Hz, echo train length 16, FOV=230mm2, matrix size=384×384, slice thickness 5mm, and TSLs=1, 20, 40, 60, and 80ms. One fully sampled dataset was acquired and was retrospectively undersampled with the designed undersampling mask. Two prospective datasets were also acquired at a net acceleration factor of 4.48.


Figure 2 shows the T-weighted images at TSL=1ms reconstructed using SCOPE with variable (VAR) and constant (CR) rates sampling mask at different acceleration factors from retrospectively undersampled data. The corresponding error maps are also shown for comparison. The images using VAR show fewer aliasing artifacts (green arrows) and has lower error than those using CR. The derived T maps using VAR are more accurate than using CR(Figure 3). Figure 4 shows T maps derived using L+S7 and SCOPE methods from the prospectively undersampled data. Obvious aliasing artifacts (green arrows) can be seen in the L+S T maps.


The proposed method offers better performance than the existing methods in both retrospective and prospective experiments, and can significantly reduce the scan time of T mapping. This technique might help facilitate fast T mapping in clinics.


This work is supported in part by the National Natural Science Foundation of China under grant nos. 61771463 and 61471350, National Key R&D Program of China nos. 2017YFC0108802.


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Figure 1. The proposed variable rate undersampling mask (a) and the constant acceleration rate undersampling mask (b) in the ky-TSL space for a net acceleration factor R=3.19. In (a), the acceleration rates for short TSLs are lower than those for long TSLs. The percentages of fully sampled k-space center lines also vary for different TSLs ( [0.15,0.13,0.13,0.12,0.12]). While in (b), the acceleration rates and the percentages of fully sampled k-space center lines for all TSLs are the same.

Figure 2. The T-weighted images at TSL=1ms reconstructed using SCOPE with variable (VAR) and constant (CR) rates sampling mask at different acceleration factors (R=3.19, 4.48 and 5.76) from retrospectively undersampled data. The corresponding error maps are also shown for comparison.The reference image is obtained from the fully sampled k-space data.

Figure 3. T maps using SCOPE with variable (VAR) and constant (CR) rates sampling mask at different acceleration factors (R=3.19, 4.48 and 5.76).The reference map is estimated from the fully sampled k-space data.The numbers denote the nRMSEs of corresponding T maps.

Figure 4. T maps estimated from the prospectively undersampled data at a net acceleration factor of R=4.48 using L+S and SCOPE methods. The reference map is estimated from the fully sampled k-space data.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)