Novel diffusion-based models for image restoration and interpolation
This concise, well-written monograph presents state-of-the art of nonlinear PDE-based filtering methods and image impainting techniques. Linear, nonlinear second-order and forth-order diffusion-based approaches, proposed mainly by the author, together with their hybrids for image denoising and impainting tasks are described. Presented in the book PDE-based denoising and impainting models are well-posed. They have some weak unique solutions that are computed using some iterative numerical algorithms applied to the finite-difference models. All the discretization schemas for PDE-models described in this book are consistent, stable and fast convergent to the solution of a suitable PDE-model. The described methods have been experimentally checked on a number of test images and compared to the other existing methods. Performance of the method was assessed by using standard quality measures of images such as PSNR, MSE, Structural Similarity Index (SSIM) and Norm of the Error Image. Advantages and disadvantages of the considered methods are also discussed. The book can be recommended to students and scientists working in the area of mathematics, computer science and electrical engineering. The readers of the book should have a basic knowledge in PDEs, numerical analysis and digital image processing.
scientific article; zbMATH DE number 6921110