High quality digital images are widely used nowadays. However, most observed images deteriorate during transformation, transmission and recording processes. Image restoration has been extensively investigated as a crucial step in image processing and numerous image enhancement techniques exist in the literature. The focus of this talk is on a PDE-based approach. The degradation of an image is considered as the result of two phenomena. One is deterministic due to the defects of the imaging system, such as blur created by an incorrect lens adjustment or by motion. The other is random due to the noise from any signal transmission. Let u0(x,y)be the pixel value (representing the intensity) of an initial low quality image and u(x,y)be the pixel value of a de-blurred and de-noised image for (x,y)∈Ω. A commonly used model assumes thatu0=Ru+η, with η being a Gaussian noise and R being a linear operator (convolution)representing the blur. Analytically determiningufromu0is an ill-posed inverse problem. We will talk about how to properly build PDE-based deblurring and de-noising filters to numerically achieve desired image resolution. This talk will be accessible to a general audience with some intuition and reasonable knowledge about partial differential equations.