Alexey V. Dimov^{1}, Nanyque A. Boyd^{2}, Keigo Kawaji^{2,3}, and Timothy J. Carroll^{1}

Rosette k-space sampling is an attractive tool for a variety of applications such QSM, DCE, etc. However, as many non-Cartesian acquisition schemes, rosette is highly susceptible to the system-specific gradient delays. We present a robust technique utilizing intrinsic symmetries of multi-shot rosettes, which allows to reconstruct images with minimal artifacts due to misalignment of the k-space points.

The proposed method utilizes intrinsic symmetries in multi-shot multi-echo rosette with even number of acquired arms. In particular, for any $$$i<N/2$$$, arms $$$i$$$ and $$$i+N/2$$$ are traversing the center of the k-space in the opposite directions and in tangential manner (Fig 2). Under ideal conditions, values measured along the rosette spokes belonging to these arms should be aligned in the k-space center. If, however, imperfect gradient timing is present, spokes’ phase and magnitude profiles will differ by a noticeable shift $$$\delta$$$ (Fig 3). This shift can be estimated through a cross-correlation of analysis of the tangential spokes and eliminated prior gridding.The algorithm of the proposed correction method can be summarized as follows:

- Split $$$N$$$ arms into $$$N/2$$$ arm pairs
- For each resulting pair of spokes $$$\{S_1, S_2\}$$$, calculate correlation $$$c = FT\{|S_1|\}\cdot FT\{|\tilde{S_2}|\}^*$$$. Here "~" denotes inversion ("flip") of the spoke points, and $$$FT\{\}$$$ is Fourier transform.
- Estimate slope $$$\alpha$$$ in the phase of $$$c$$$
- Shift each of the spokes by $$$\frac{L\alpha}{4\pi}$$$

**Experimental validation**

2D multi-shot rosette sequence was implemented on a 3T MR platform (Philips Achieva). A phantom dataset was acquired using a 64-arm rosette sequence (FOV = 22 cm, Slice thickness = 5 mm, # Slices = 1, TR = 24-30 ms, TE = 0.8-1.2ms, 24 echoes). No parallel imaging was used. A volunteer data was additionally acquired using similar scan parameters.The gridding reconstruction, implemented offline using MATLAB (The Mathworks, Natick, MA) with CUDA-PTX graphical processing unit acceleration (NVIDIA, Santa Clara, CA) of the original data and data corrected using the proposed technique was performed. Image magnitude, phase, and presence of off-resonance artifacts was examined using region-of-interest analysis.

- Noll DC, et.al., Magn Reson Med. 1998 May;39(5):709-16
- Peters DC, et al., Magn Reson Med. 2003 Jul;50(1):1-6.

Figure 1. Structure of a multi-echo multi-arm rosette

Figure 2. Rosette trajectory in k-space. Note the tangential passing of two rosette arms at each crossing of the k-space origin.

Figure 3. (a) Crossing of the k-space center by a set of rosette spokes’ pairs; (b) Magnitude and (c) phase profiles of the spokes. Note the shift δ in the data prior the correction.

Figure 4. Comparison of results of processing of the original and corrected phantom data, and results of reconstruction from the corrected volunteer data.

Figure 5. Magnitude and phase profiles of the spokes after correction. Notice that the shift due to gradient delays was successfully eliminated.