Statistical optimum 2D random sampling for Compressed Sensing MRI

Compressed sensing (CS) is a groundbreaking method that enables the restoration of a high signal-to-noise ratio (SNR) image reconstructed from a small amount of collected data. The application of CS leads to rapid imaging for magnetic resonance imaging (CS-MRI) because image reconstruction is possible from a small amount of k-space data. In CS-MRI, the sampling pattern is an important factor because acquired data is randomly sampled. In this study, we investigated the influence of the acquisition signal pattern on the reconstructed images. The simulated random signal patterns of the 2D phase encode in the 3D k-space are Gaussian sampling using the 2D Gaussian probability density function and circular sampling using the full circular sampling in the low-frequency domain and uniformly random sampling in the high-frequency domain. We demonstrated CS-MRI reconstruction using two numerical phantoms, the 3D Shepp-Logan phantom and T1 weighted BrainWeb phantom, with 20 dB Gaussian noise added to each. We performed simulations while changing the full width at half maximum (FWHM) for the Gaussian sampling case and the radius of the circle for the circular sampling case. The result of our simulation for Gaussian sampling was that the optimum FWHM was present under all acceleration rates. When the acceleration rate was set to x5.0, SSIM was the best for each phantom when FWHM was 0.25. On the other hand, the optimum radius was different for each phantom in the circular sampling. In the Shepp-Logan phantom, there was an optimum radius with random sampling at low acceleration rates. However, for the T1 weighted phantom, there was an optimum radius without random sampling for all acceleration rates. The images for Gaussian sampling showed an overall better evaluation value of SSIM than that for circular sampling. From these results, it was suggested that stable reconstructed images of CS-MRI can be obtained by using Gaussian sampling with FWHM suitable for acceleration rate.