FFT 5/24/21: Demetrio Labate - Image inpainting problem using sparse multiscale representations
Image inpainting is an image processing task aimed at recovering missing blocks of data in an image or a video. In this talk, I will show that sparse multiscale representations offer both an efficient algorithmic framework and a well-justified theoretical setting to address the image inpainting problem. I will start by formulating inpainting in the continuous domain as a function interpolation problem in a Hilbert space, by adopting a formulation previously introduced by King et al. [2014]. As images found in many applications are dominated by edges, I will assume a simplified image model consisting of distributions supported on curvilinear singularities. I will prove that the theoretical performance of image inpainting depends on the microlocal properties of the representation system, namely exact image recovery is achieved if the size of the missing singularity is smaller than the size of the structure elements of the representation system. A consequence of this observation is that a shearlet-based image inpainting algorithm - exploiting their microlocal properties - significantly outperforms a similar approach based on more traditional multiscale methods. Finally, I will apply this theoretical observation to improve a state-of-the-art algorithm for blind image inpainting based on Convolutional Neural Networks.