Towards real-time 3D geometric nonlinear diffusion filter and its application to CT and MR imaging

We propose two near real-time nonlinear anisotropic diffusion filtering (NADF) methods for the 2D and 3D X-ray computed tomography (CT) and magnetic resonance (MR) image denoising. Typically, NADFs are preferred for the medical image denoising due to its edge preserving feature though they are computationally expensive. Recently, a computation-time efficient 2D NADF has been proposed which uses local pixel intensity-based geometric parameters for diffusion. But it has limitations resulting from (i) its assumption that the neighboring pixels are non-noisy while deciding on an interrogated pixel being noisy or not, and (ii) its confinement of working only on a 2D image. Motivated from this, we propose an improved 2D NADF method that uses additional neighboring pixels in an effective way to lower the noise impact on the estimated geometric parameters. We also extend our 2D method into 3D that considers all the three directions for information diffusion. The performance of the proposed methods is evaluated using a 3D synthetic phantom, and in vivo CT and MR data which demonstrates an average signal-to-noise-ratio-gain improvement of approximately 58% in 2D and 96% in 3D phantom data, and approximately 79% in 2D and 127% in 3D in vivo data, compared to the state-of-the-art method.