Motion artifacts are extremely common in clinical MRI, and present one of the biggest challenges in MRI. The recently introduced Magnetic Resonance Fingerprinting (MRF)^[1] has been shown to be less sensitive to motion than conventional imaging through the use of pattern matching. However, the template matching^[1] based pattern matching algorithms used in most initial implementations are still susceptible to patient motion primarily occurring in the early stages of the acquisition. The goal of this study is to develop a reconstruction algorithm for MRF that is explicitly insensitive to imaging artifacts from motion. Here we present an algorithm based on robust fitting algorithm and image registration algorithm to estimate and compensate motion.

The pattern matching algorithm was reformulated as a least squares linear regression problem. In this framework, the fingerprint with the least root mean square fitting error (RMSE) was used as the matched fingerprint. To improve the robustness of dictionary matching algorithm, we extended the iterative re-weighted least squares fitting method, which is known to be robust with respect to outliers and errors^[2]. The flow of the proposed motion compensated robust fingerprinting (MORF) reconstruction algorithm is as follows:

1. Robust dictionary matching. Dictionary matching using robust regression is performed for each pixel within region of interest. The signal evolution of each pixel is replaced by the matched fingerprint, appropriately scaled by the estimated proton density value.

2. Parallel imaging sub-problem. For each individual timeframe the following optimization problem of motion-compensated regularized SENSE^[3] was solved:

$${\bf m^*}=\arg \min_{\bf m}\parallel F_u C_i R^{-1} {\bf m}-{\bf d}\parallel_2+ \lambda_1 \psi({\bf m})$$

where $$${\bf m}$$$ is the motion-registered frame after coil combination, $$$R$$$ is the motion registration operator, $$${C_i}$$$ is the individual coil sensitivity profile, $$${\bf d}$$$ is the measured k-space data, $$$F_u$$$ is the undersampled non-uniform Fast Fourier Transform (nuFFT), $$${\lambda_1}$$$ is the regularization weight and $$${\psi}$$$ is the regularization transform.

3. Motion estimation sub-problem. Timeframes with error between $$${\bf m^*}$$$ and $$${\bf m}$$$ above a selected threshold value (heuristically selected as 9%) were considered to be motion corrupted. Displacement fields were estimated using rigid-body image registration for motion corrupted frames.

Steps 1 and 2 were repeated until convergence was achieved. Step 3 was empirically selected to perform every even iteration after the first five. (The initial frames all show significant residual aliasing artifacts and are thus unsuitable for image registration.) After convergence, step 1 was performed as the final step of the reconstruction algorithm. Equation 1 was solved using non-linear conjugate-gradient algorithm^[4] with total variation as the regularization operator. In this study, image registration was performed using MATLAB (The Mathworks, Inc., Natick, MA) 2014b’s built-in functions with rigid-body motion as the registration transform.

Numerical phantoms (Shepp-Logan and brain), generated using T1, T2 and PD maps from MNI brain atlas^[5], were used for evaluation of the proposed algorithm. For assessment of the algorithm, rigid motion was simulated in the numerical phantoms. A rotational motion of 45⁰ was introduced in the initial 215 frames from a total of 1000 frames (frames 1 to 20: presenting tilt from 0⁰ to 45⁰; frames 21 to 195: stationed at 45⁰; frames 196 to 215: presenting tilt from 45⁰ to 0⁰). A variable density spiral (VDS) trajectory, with fully sampled center of k-space and edge of k-space undersampled by a factor of 48, was used for these simulations. The motion corrupted fully sampled images were forward sampled using nuFFT^[6] to estimate the undersampled (1 spiral leaf; R=48) k-space measurements. For comparison, the simulated data was reconstructed using the previously presented iterative multi-scale^[7] (IMS-MRF) reconstruction algorithm.

Figure 1,2 and 3 shows the T1 and T2 estimation results from the simulations using Shepp-Logan (figure 1) and brain (figure 2 and 3) phantoms. The maps estimated using IMS-MRF present residual motion artifacts (RMSE for Shepp-Logan: T1=61.09% and T2=31.77%; Brain: T1=77.95% and T2=11.14%). However, maps using MORF are closer to ground truth and present minimal errors (RMSE for Shepp-Logan: T1=3.69% and T2=2.57%; Brain: T1=8.07% and T2=4.70%) even though 21.5% of the data is motion corrupted during the early stages of the acquisition. Figure 4 shows the reconstructed, ground truth and undersampled images corresponding to the frames with simulated motion. Figure 5 shows example signal evolution curves from a pixel affected by motion. It illustrates the robustness of proposed algorithm to motion and the capability of performing signal recovery.The proposed MORF reconstruction algorithm noticeably decreases the sensitivity of MRF to motion. The algorithm could potentially be used by itself for motion estimation for applications such as estimation of cardiac function.