Pseudo-Polar Fourier Transform based Compressed Sensing MRI

Objective: The use of radial k-space trajectories has drawn strong interest from researchers for its potential in developing fast imaging methods in Magnetic Resonance Imaging (MRI). Compared with conventional Cartesian trajectories, radial sampling collects more data from the central k-space region and the radially sampled data are more incoherent. These properties are very suitable for compressed sensing (CS) based fast imaging. When reconstructing under-sampled radial data with CS, regridding and inverse-regridding are needed to transfer data between the image and frequency domains. In each CS iteration, two dimensional (2D) interpolations are implemented twice in the regridding and inverse-regridding, introducing errors and undermining reconstruction quality. To overcome these problems, a radial-like pseudo-polar (PP) trajectory is proposed for the CS MRI applications. The pseudo-polar trajectory preserves all the essential features of radial trajectory and allows an image reconstruction with PP Fast Fourier Transform (FFT) instead of interpolations. This paper attempts to investigate the performance of pseudo-polar trajectory based CS-MRI. Methods: In CS-based image reconstruction, the transformation of pseudo-polar sampled k-space data into the image domain is realized through PPFFT, which is based on the standard one dimensional (1D) FFT and the Fractional Fourier Transform (FRFT). To evaluate the effectiveness of the proposed methods, both numerical and experimental data are used to compare the new methods with conventional approaches. Results: The proposed method provided high-quality reconstruction of the MR images with over 2 dB gain in peak signal-to-noise ratio (PSNR) while keeping structural similarity over 0.88 in different situations. Conclusion: Compared with the conventional radial sampling based CS MRI methods, the proposed method achieves a more accurate reconstruction with respect to image detail/edge preservation and artifact suppression. Significance: The successful implementation of the pseudo-polar sub-sampling based CS scheme provides a practical and accurate CS-based rapid imaging method for clinical applications