Recent progress in dynamic MRI propose low-rank plus sparse (L+S) matrix decomposition for image reconstruction from undersampled data ^1,2. The L+S method has been successfully applied to multiple applications including cardiac MRI, perfusion, angiography ³ and recently to denoise resting-state fMRI data ⁴, suggesting that it might be promising for accelerating the task-based fMRI. We propose to use a 3D Stack of Spirals (SoS) sequence and achieve acceleration via excluding phase encoding planes in the k_z-t domain. We then use the L+S method to (1) reconstruct aliasing artifact corrected images and (2) improve statistical significance of activation due to the increased temporal resolution. We further hypothesize that activation maps in S are a more realistic representation of the true BOLD signal after eliminating the physiologic noise in the L component.

The L+S reconstruction is defined by the following convex optimization problem:

$$\arg \min_{L,S} \frac 12 \parallel E(L+S)-d\parallel_F^2 +\lambda_L\parallel L\parallel_* +\lambda_S\parallel S\parallel_1$$

where E is the encoding operator, $$$d$$$ is the k-space data, $$$T$$$ is the sparsifying transform for $$$S$$$, $$$\parallel . \parallel_*$$$ and $$$\parallel . \parallel_1$$$ are the nuclear norm and $$$l_1$$$ norm of the matrices $$$L$$$ and $$$TS$$$. $$$\lambda_L$$$ and $$$\lambda_S$$$ are the regularization parameters that balance the contributions of $$$L$$$ and $$$S$$$. $$$L$$$ represents the highly correlated background information that slowly changes over time (cardiac pulsation, respiratory movement), while $$$S$$$ captures spatially localized dynamic information. Linear combination of $$$L$$$ and $$$S$$$ results in a matrix $$$M$$$ representing the slowly changing background with localized dynamic components.

We applied the L+S method to fMRI data on a healthy adult volunteer on a 3T scanner (Siemens, Tim Trio) with a 12-channel head coil. A 3D SoS trajectory was used to acquire fully sampled fMRI data in the whole brain. The imaging parameters were: FOV=22 cm, 64x64 matrix resolution, 40 2 mm thick slices, TR/TE=50/30ms, flip angle 15 degrees and 120 temporal frames. The paradigm was a flashing checkerboard consisting of four 30 sec “on” and 30 sec “off” blocks for a total duration of 4 minutes. The data were then retrospectively undersampled with x2 and x4 factors in the k_z-t domain by fully sampling the centre lines of k-space and randomly excluding remaining planes at every time point (Fig. 1). For x4 undersampling, three different sampling patterns were examined. After the pattern providing the best reconstruction result was selected, a prospectively 4x undersampled fMRI scan was performed providing increased temporal resolution of 480 time points. All L+S reconstructions were performed using a temporal FFT as a sparsifying transform. Statistical analysis of the BOLD based activation was accomplished using a generalized linear model (GLM).

Fig. 2 shows L+S reconstruction results of one slice within the visual cortex with overlaid activation scaled from t=6 to 8. Fig. 2 (a) is fully sampled data, (b) data retrospectively under sampled x2, (c-e) x4 undersampling using three different sampling patterns (as shown), and (f) prospectively undersampled data using a 4x acceleration. For retrospective undersampling, the L+S algorithm was able to eliminate aliasing artifacts and reconstruct structural brain images in the L component and retrieve BOLD signal in the S and M components that is only partially seen in the B images computed from the undersampled data. The activation patterns from the x2 and x4 retrospectively undersampled data are qualitatively consistent to that of the fully sampled data. For prospective under sampling, although L+S was less successful in eliminating artifacts, good recovery of the activation maps was observed. Fig. 3 shows reconstruction of multiple slices in the vicinity of the visual cortex from the 4x prospectively accelerated fMRI scan shown in Fig. 2 (f). Better statistical significance of activation regions is observed in the S components compared with the B images. Fig. 4 shows different types of separation into L and S components using different weights of the regularization parameters. It can be seen that L+S decomposition is highly sensitive to regularization values. Finally, Fig. 5 illustrates GLM fitting into the average BOLD signal across all activated voxels in the prospective data. It can be seen that physiological "slow drift" noise is absorbed by the L component, while S mainly captures the localized time-varying BOLD signal. Furthermore, spectral analysis confirms that the activation peak is absorbed by the S component as indicated by the arrow.

An approach for prospectively accelerating fMRI using an under sampled 3D SoS acquisition and L+S image reconstruction is presented. Experimental fMRI results demonstrate the ability of the approach in obtaining aliasing artifact corrected functional images with improved statistical significance of the activation maps.