RESUMO
Diffusion process is widely applied to digital image enhancement both directly introducing diffusion equation as in anisotropic diffusion (AD) filter, and indirectly by convolution as in Gaussian filter. Anomalous diffusion process (ADP), given by a nonlinear relationship in diffusion equation and characterized by an anomalous parameters q, is supposed to be consistent with inhomogeneous media. Although classic diffusion process is widely studied and effective in various image settings, the effectiveness of ADP as an image enhancement is still unknown. In this paper we proposed the anomalous diffusion filters in both isotropic (IAD) and anisotropic (AAD) forms for magnetic resonance imaging (MRI) enhancement. Filters based on discrete implementation of anomalous diffusion were applied to noisy MRI T2w images (brain, chest and abdominal) in order to quantify SNR gains estimating the performance for the proposed anomalous filter when realistic noise is added to those images. Results show that for images containing complex structures, e.g. brain structures, anomalous diffusion presents the highest enhancements when compared to classical diffusion approach. Furthermore, ADP presented a more effective enhancement for images containing Rayleigh and Gaussian noise. Anomalous filters showed an ability to preserve anatomic edges and a SNR improvement of 26% for brain images, compared to classical filter. In addition, AAD and IAD filters showed optimum results for noise distributions that appear on extreme situations on MRI, i.e. in low SNR images with approximate Rayleigh noise distribution, and for high SNR images with Gaussian or non central χ noise distributions. AAD and IAD filter showed the best results for the parametric range 1.2 < q < 1.6, suggesting that the anomalous diffusion regime is more suitable for MRI. This study indicates the proposed anomalous filters as promising approaches in qualitative and quantitative MRI enhancement.
