Reducing the effects of noise in MRI reconstruction

Fourier methods are a natural choice for reconstructing magnetic resonance images (MRI). Unfortunately, however, due to the many different tissues normally present in each scan, the Gibbs ringing artifact often hinders accurate reconstruction. These effects are exacerbated in the presence of random noise, which is inherent in MRI spectral data. Recently, numerical edge detection and reconstruction methods have been developed that effectively reduce the Gibbs oscillations while maintaining high resolution accuracy at the edges. This paper addresses the issue of noise in MRI reconstruction and its effects on the ability to recover the image. The numerical method we apply here not only recovers the images with very high accuracy, but it is also robust in the presence of noise.