  We develop an algorithm for single-image superresolution of remotely sensed
data, based on the discrete shearlet transform. The shearlet transform extracts
directional features of signals, and is known to provide near-optimally sparse
representations for a broad class of images. This often leads to superior
performance in edge detection and image representation when compared to
isotropic frames. We justify the use of shearlets mathematically, before
presenting a denoising single-image superresolution algorithm that combines the
shearlet transform with sparse mixing estimators (SME). Our algorithm is
compared with a variety of single-image superresolution methods, including
wavelet SME superresolution. Our numerical results demonstrate competitive
performance in terms of PSNR and SSIM.
