Eun Hee Kim

High quality digital images are widely used nowadays. However, mostobserved images deteriorate during transformation, transmission andrecording processes. Image restoration has been extensively investigated asa crucial step in image processing and numerous image enhancementtechniques exist in the literature. The focus of this talk is on a PDE-basedapproach. The degradation of an image is considered as the result of twophenomena. One is deterministic due to the defects of the imaging system,such as blur created by an incorrect lens adjustment or by motion. Theother is random due to the noise from any signal transmission. Letu0(x,y)be the pixel value (representing the intensity) of an initial low qualityimage andu(x,y)be the pixel value of a de-blurred and de-noised imagefor(x,y)∈Ω. A commonly used model assumes thatu0=Ru+η, withηbeing a Gaussian noise andRbeing a linear operator (convolution)representing the blur. Analytically determiningufromu0is an ill-posedinverse problem. We will talk about how to properly build PDE-basedde-blurring and de-noising filters to numerically achieve desired imageresolution. This talk will be accessible to a general audience with someintuition and reasonable knowledge about partial differential equations.