Gibbs ringing artifact and spatial correlation in MRI

Gibbs ringing artifact is a type of image distortion which manifests itself as spurious ringing around sharp edges. It is an inevitable result of truncating the Fourier Series due to missing of high-frequency data or finite sampling. Most studies on Gibbs ringing artifact focus on its effect on image resolution. Our study will show its link to spatial correlation in the image. Based on the theory of signal processing and statistical communication, three types of MR signals and two types of k-space samples are studied. k-space samples in MRI data acquisition are shown to be independent Gaussians. Based on Fourier Transform (FT) and Filtered Backprojection (PR) image reconstruction algorithms and using Linear system theory, pixel intensities in the reconstructed MR image are shown to be asymptotically independent. The quantitative measures of this local dependence are derived. Our study reveals that finite k-space sampling introduces pixel-to-pixel correlation in the reconstructed MR image. This kind of data acquisition protocol and FT/PR reconstruction turn independent k-space samples into correlated image pixels. This finding and the derived formulae provide a basis for further development in MRI statistical study and stochastic model-based MR image analysis strategies.