A Fast Algorithm to Reduce Gibbs Ringing Artifact in MRI

In magnetic resonance imaging, a finite number of k-space data are often collected in order to decrease the acquisition time. The partial k-space data lead to the famous Gibbs ringing artifact with Fourier transform method. The Gegenbauer reconstruction method has been shown to effectively eliminate the Gibbs ringing artifact and restore high resolution. However, the disadvantages of using the Gegenbauer method are more computational time and complicated the choice of parameters. In this paper, we improve the Gegenbauer method by introducing the inverse polynomial reconstruction method and replacing the Gegenbauer polynomials with the Chebyshev polynomials. The new method effectively reduces the reconstructed error and computational cost without any requirement for selection of parameters. Additionally, we present an improved edge detection method which can achieve more accurate edge and make our new reconstruction method more efficient. The proposed method is verified with experiment of the artifact removal