Image enhancement through complex conduction coefficient modifications

One important term in the diffusion equation applied to image processing is the conduction coefficient. It could be a real or complex function, depending on the chosen diffusion processes. A modification in the form of the application of filter convolution to the real-value conduction coefficient has been recommended for the improvement of the signal-to-noise ratio and the speed by which the diffusion is performed. In this study, the developments of the approximately circularly symmetric two-dimensional Lagrange filter and the Teager operator are presented. They are proposed here for the modification of the complex-value conduction coefficient for the improvement of the image diffusion process. Performance of the proposed modifications is evaluated through simulation and the use of three metrics. Experimental results suggest the validity and applicability of the proposed modifications.