Single-Image Superresolution Through Directional Representations

We develop a mathematically-motivated algorithm for image superresolution, based on the discrete shearlet transform. The shearlet transform is strongly directional, and is known to provide nearoptimally sparse representations for a broad class of images. This often leads to superior performance in edge detection and image representation, when compared to other isotropic frames. We justify the use of shearlet frames for superresolution mathematically before presenting a superresolution algorithm that combines the shearlet transform with the sparse mixing estimators (SME) approach pioneered by Mallat and Yu. Our algorithm is compared with an isotropic superresolution method, a previous prototype of a shearlet superresolution algorithm, and SME superresolution with a discrete wavelet frame. Our numerical results on a variety of image types show strong performance in terms of PSNR.