Efficient Direct Summation Reconstruction for Radial & PROPERLLER MRI using the Chirp Transform Algorithm

Yanqiu Feng¹, Yanli Song¹, Cong Wang¹, Taigang He², Xuegang Xin¹, Wufan Chen¹

Direct Fourier transform (DFT) could reconstruct MR image from non-Cartesian data with high precision. However, the high computation complexity makes DFT impractical for clinical application. Up to now, the published "FFT" algorithms for non-equispaced data do not strictly compute the DFT of nonequispaced data, but rather some approximation. In this work, an efficient algorithm for DFT using the Chirp Transform Algorithm (CTA) was proposed to reconstruct MR image from non-Cartesian trajectories consisting of lines with equispaced points such as radial or PROPERLLER sampling. The proposed CTA-DFT algorithm is demonstrated to be significantly faster than DFT while keeping the same accuracy.