  In this work, a gray level indicator based non-linear telegraph diffusion
model is presented for multiplicative noise removal problem. Most of the
researchers focus only on diffusion equation-based model for multiplicative
noise removal problem. The suggested model uses the benefit of the combined
effect of diffusion equation as well as the wave equation. Wave nature of the
model preserves the high oscillatory and texture pattern in an image. In this
model, the diffusion coefficient depends not only on the image gradient but
also on the gray level of the image, which controls the diffusion process
better than only gradient-based diffusion models. Moreover, we prove the
well-posedness of the present model using Schauder fixed point theorem.
Furthermore, we show the superiority of the proposed model over a recently
developed method on a set of gray level test images which are corrupted by
speckle noise.
