Radial-acquisition(RA) imaging is recently gaining more popularity in MR community due to its ability of enabling a shorter TE as well as being tolerant to motion artifacts [1]. For RA image reconstruction, both fast Fourier transform (FFT) via gridding and filtered back-projection (FBP) are available. However, for 3D RA, FFT is dominantly used because 3D FBP is known to need a much longer reconstruction time. If this processing-time issue is resolved, 3D FBP can be promising in the case of FID sampling that needs to estimate the true k=0 point, or echo sampling with mis-centering of k-space in the presence of gradient delays or B0 inhomogeneities [2], since the signal at k=0 is not required in FBP due to the ‘M-filter’ intrinsically needed in FBP reconstruction. Here we propose a strategy that can significantly reduce the reconstruction time of 3D FBP in combination with a new RA scheme. Performance of the proposed method was demonstrated in phantom and human brain imaging at 3T.

For the conventional 3D FBP, a set of planar projections are needed for back-projection, which are obtained using the 3D projection slice theorem, i.e., by acquiring an echo or a FID signal along the (θ,Φ) direction and performing FT (Fig. 1) [3]. In this case, the most time-consuming process occurs when the ‘2D’ planar projections are back-projected for ‘3D’ reconstruction, which is called ‘Direct 3D FBP’ in Fig. 1B [4]. In contrast, only two steps of ‘2D FBP’ are used for final 3D reconstruction in the proposed method (Fig. 2B), which dramatically reduces the processing time. For this purpose, radial data need to be collected in a series of circular trajectories (Fig. 2A) and each circular trajectory is attained by increasing Φ between 0 and 2π for each given θ (0≤θ≤π).

For demonstration, phantom and human brain were scanned at Siemens 3T(Trio) using a 4-channel volume coil. For all experiments, a 3D radial gradient-echo sequence was used acquiring a partial echo with a minimum TE. All data was collected using the proposed radial-acquisition strategy depicted in Fig. 2A. Scan parameters were: TR/TE = 3/0.22ms, FOV = 300m³, FA = 5°, number of projections = 64.8k, matrix size = 600³(oversampled), isotropic resolution = 1mm³.

Images were reconstructed offline using a home-built MATLAB (ver. 8.2.0; R2013b) program on a workstation equipped with an Intel-Xeon CPU (3.50GHz processor) and an NVIDIA Quadro K600 graphics card. For comparison, reconstruction was performed using 3D FFT, direct 3D FBP, and the proposed method. For the 3D FFT, a gridding procedure was coded in C language to reduce the processing time. MATLAB internal functions of ‘iradon’ and ‘imrotate’ were used for back-projection and matrix rotation, respectively. To validate the robustness of the FBP in mis-centering of k-space, some echo peaks of the original data were shifted in order to have a larger variation. While the maximum variation of the echo-peak positions in the original data was 2 sample points (= 7.6μs), that in the echo-peak-shifted data was 17 sample points (= 64.6μs).

Figure 3 shows the axial slices of an ACR phantom and human brain reconstructed using the 3D FFT, the direct 3D FBP, and the proposed method. 3A~3D were from the original data and 3E~3J from the echo-peak-shifted data. When mis-centering of k-space is small, the proposed FBP showed almost same image quality as the 3D FFT. However, with large mis-centering, the 3D FFT showed typical mis-centering artifacts such as contrast variations from the center to the periphery, whereas both 3D FBP methods provided as good an image quality as C and D with small mis-centering, showing their tolerance to mis-centering of k-space.

In terms of processing time (Table 1), the proposed method took only a 1min 25sec to reconstruct 600³ matrix size, which was much shorter (by a factor of 225) than that of the direct 3D FBP (= 318min 45sec). Even the 3D FFT using gridding took almost 10 times longer reconstruction time than the proposed method.

We suggested an acquisition and reconstruction strategy for fast 3D FBP. The results show that the proposed method is able to dramatically shorten the reconstruction time, when compared to the direct 3D FBP and even the 3D FFT using gridding. Once the 3D FBP is practically available in terms of the processing time as shown here, it will be very useful in 3D RA imaging including FID sampling, especially when gradient delays or eddy currents cause significant mis-centering of k-space, or in the presence of large field inhomogeneities.