An inverse mathematical technique for improving the sharpness of magnetic resonance images

Magnetic Resonance Imaging (MRI) is a powerful imaging modality with highly specific applications in medicine. However, certain series and sequences of MRI do not produce images with good acuity. Widely-used sharpening algorithms like Shock Filter (SF) and Unsharp Masking (UM) do not provide output images with appreciable sharpness-to-noise ratio. Output images of UM are prone to discontinuity artefact. A noise-robust sharpening algorithm to enhance acuity of MR images termed as Nonlinear Amplification of Spatial Derivative (NASD) that does not have the issue of discontinuity artefact is introduced in this paper. In the NASD, the enhanced image is estimated from the amplified spatial derivative in an inverse way. To avoid the amplification of noise, the amplification factor at any pixel location is calculated from a nonlinear function of the mean of the absolute values of the gradients along eight different orientations at that location. On hundred test images, the sharpness-to-noise ratio exhibited by NASD, SF and UM are 0.0963 ± 0.0400, 0.1642 ± 0.0967 and 0.2851 ± 0.1610. The computation time (in seconds) of NASD, SF and UM are 0.0330 ± 0.0031, 0.0452 ± 0.0390 and 0.0554 ± 0.0112. The NASD exhibits higher values of sharpness-to-noise ratio than SF and UM. NASD is able to sharpen the edges in the input image without amplifying noise and it is computationally fast like SF and UM.