Quantitative comparison of Gegenbauer, filtered Fourier, and Fourier reconstruction for MRI

Magnetic Resonance Images are reconstructed from a finite number of samples in k-space. The accuracy of these reconstructions are crucial for segmentation and diagnosis. However, the nature of the reconstruction leads inevitably to Gibbs ringing. In this paper, we quantitatively compare the filtered Fourier and Gegenbauer ringing-suppressing reconstruction methods. The Gegenbauer method yields an order of magnitude better MSE than the other approaches we consider, and a 10 dB improvement in PSNR. These results confirm the Gegenbauer reconstruction as the most accurate choice in inverse problems where data is reconstructed from a finite number of Fourier coefficients.