Fast undersampled functional magnetic resonance imaging using nonlinear regularized parallel image reconstruction

Abstract

In this article we aim at improving the performance of whole brain functional imaging at very high temporal resolution (100 ms or less). This is achieved by utilizing a nonlinear regularized parallel image reconstruction scheme, where the penalty term of the cost function is set to the L(1)-norm measured in some transform domain. This type of image reconstruction has gained much attention recently due to its application in compressed sensing and has proven to yield superior spatial resolution and image quality over e.g. Tikhonov regularized image reconstruction. We demonstrate that by using nonlinear regularization it is possible to more accurately localize brain activation from highly undersampled k-space data at the expense of an increase in computation time.

Figure 1. Design of the trajectory.

End points of the radial sections of the trajectory (A) and 3D plot of the k-space sampling pattern (B).

Figure 2. Sample reconstructions.

Sum of square image of the reference data (A), a sample reconstruction using the Tikhonov regularization (B) and the sample reconstruction using the l₁-norm regularized reconstruction (C).

Figure 3. Point spread functions.

A PSF for the 3D rosette trajectory (A) and for the 3D SSR (B) in the Tikhonov regularized case in comparison to a local PSF of the 3D SSR trajectory using the L₁-norm regularized reconstruction (C).

Figure 4. Simulation of brain activation.

Results of the simulation: Tikhonov reconstructed time series (A) and L₁-norm regularized reconstruction (B).

Figure 5. Comparison of activated brain areas for different reconstructions.

Penalty terms: Tikhonov (column 1), l₁-norm (column 2) and l₁-norm in the wavelet domain (column 3) for visual checkerboard stimulation (row A) and bilateral finger tapping (row B).

Figure 6. Activation map dependence on the regularization parameter.

Image reconstruction was performed using the l₁-norm penalty and the following regularization parameters: (A), (B) and (C).

Figure 7. Comparison with additional off-resonance correction.

Sample L₁-norm-penalized reconstruction without (A) and with additional off-resonance correction (B).Activation map without (C) and with (D) off-resonance correction. A spatial map of the off-resonances in Hz (E) and the activation map of an EPI experiment (F).

Figure 8. Comparison of time courses.

Time course of a voxel in the visual cortex for Tikhonov (black) and l₁-norm regularized reconstruction (red). The sections with the light blue background correspond to the times when the checkerboard was switched on.