Strategies for rapid reconstruction in 3D MRI with radial data acquisition: 3D fast Fourier transform vs two-step 2D filtered back-projection

For 3D radial data reconstruction in magnetic resonance imaging (MRI), fast Fourier transform via gridding (gFFT) is widely used for its fast processing and flexibility. In comparison, conventional 3D filtered back projection (cFBP), while more robust against common radial k-space centering errors, suffers from long computation times and is less frequently used. In this study, we revisit another back-projection reconstruction strategy, namely two-step 2D filtered back-projection (tsFBP), as an alternative 3D radial MRI reconstruction method that combines computational efficiency and certain error tolerance. In order to compare the three methods (gFFT, cFBP, and tsFBP), theoretical analysis was performed to evaluate the number of computational steps involved in each method. Actual reconstruction times were also measured and compared using 3D radial-MRI data of a phantom and a human brain. Additionally, the sensitivity of tsFBP to artifacts caused by radial k-space centering errors was compared with the other methods. Compared to cFBP, tsFBP dramatically improved the reconstruction speed while retaining the benefit of tolerance to the radial k-space errors. Our study therefore suggests that tsFBP can be a promising alternative to the conventional back projection method for 3D radial MRI reconstruction.