Image Extrapolation Using Sparse Methods

Abstract

Image extrapolation is the specific application in image processing. You have to extrapolate the image for example when you want to process the given image piecewise. When the border patches are incompleted you must extrapolate them to the given size. Nowadays,some basic extrapolations, e.g. linear, polynomial etc. are used. The advanced methods are presented in this paper. We are using the algorithms that are based on finding the sparse solutions in underdetermined systems of linear equations. Three algorithms are presented for image extrapolation. First one is the K-SVD algorithm. K-SVD is the algorithm that trains a dictionary which allows the optimal sparse representation. Second one is Morphological Component Analysis (MCA) which is based on Independent Component Analysis (ICA). The last is the Expectation Maximization (EM) algorithm. This algorithm is statistics-based. These three algorithms for image extrapolation are compared on the real images.