Cross-scale predictive dictionaries

We propose a novel signal model, based on sparse representations, that captures cross-scale features for visual signals. We show that cross-scale predictive model enables faster solutions to sparse approximation problems. This is achieved by first solving the sparse approximation problem for the downsampled signal and using the support of the solution to constrain the support at the original resolution. The speedups obtained are especially compelling for high-dimensional signals that require large dictionaries to provide precise sparse approximations. We demonstrate speedups in the order of 10 − 100× for denoising and up to 15× speedups for compressive sensing of images, videos, hyperspectral images and light-field images.