Mathematical Techniques for Image Interpolation

We discuss the problem of interpolating visually acceptable images at a higher resolution. We first present the interpolation problem and why linear interpolation filters are inadequate for image data. To represent the major mathematical approaches to image processing, we discuss and evaluate five different image interpolation methods. First, we present a PDE-based method derived from the anisotropic heat equation. Next, we discuss the extension of Mumford-Shah inpainting to image interpolation. A wavelet-based method that detects edges based on correlations across sub-bands is discussed. To represent the machine learning community, we discuss a method inspired by Locally Linear Embedding (LLE) that interpolates image patches by finding close matches in a training set. Finally, we present a novel statistical filter based on Non Local (NL) Means denoising that interpolates and removes noise by using global image information.