Superresolution of Noisy Remotely Sensed Images Through Directional Representations

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 with 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 (SMEs). 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 peak-signal-to-noise ratio and structural similarity index metric.