Development and Analysis of a Class of Partial Differential Equation-Based Models: Application to Image Restoration

Abstract: Many digital image processing applications rely on the quality of the obtained images. Unfortunately, in the real scenario, due to the natural barriers of acquiring equipment or the presence of intermittent fluctuations in the medium, the images acquired by a scanner or digital camera are generally contaminated by different types of noises such as Gaussian noise, Speckle noise, Poisson noise, etc. Hence, image restoration is crucial for high-level image analysis, e.g., image segmentation, object recognition, scene understanding, etc.

In this seminar, I focus my interest in developing and analyzing a class of partial differential equations (PDEs) based models for image restoration. I start this talk with a coupled diffusion-based model for the additive Gaussian noise removal process. First, I discuss the existence and uniqueness of the weak solution of the model and then compare the image denoising performance of the model with the performance of several existing models. Next, a coupled telegraph-diffusion based model is presented for the additive Gaussian noise removal process. First, verify that the model has a unique global weak solution. Then apply this model over a set of gray-level test images to illustrate the superiority of the proposed model over the recently developed telegraph-diffusion based models. After that, a gray level indicator based nonlinear telegraph diffusion model is presented for the multiplicative speckle noise removal problem. The proposed model uses the benefit of the combined effect of the diffusion equation and the wave equation. In this method, the diffusion coefficient depends not only on the image gradient but also on the gray level of the image. First, I discuss the existence and uniqueness of the weak solution of the proposed model. Then to check the noise removal efficiency of the present model apply it over a set of gray level test images (artificially noisy image and real images) corrupted by speckle noise with different noise levels. Finally, a nonlinear coupled hyperbolic-parabolic PDE model is discussed to deal with the speckle noise removal problem. First, verify that the model has a unique weak solution. Then apply it to different gray level test images and real (SAR and Ultrasound) images. The present models show an exciting performance for image denoising.