Efficient Coupled Dictionary Learning And Sparse Coding For Noisy Piecewise-Smooth Signals: Application To Hyperspectral Imaging

Given two datasets that belong to different feature spaces and both correspond to the same underlying phenomenon, the scope of coupled dictionary learning is to compute two dictionaries, one for each dataset, so that each dataset is approximated using the respective dictionary but the same sparse coding matrix. In this work, the focus is on a particular, yet widespread, form of this problem in which the datasets correspond to slowly varying (piece-wise smooth) signals, and the measurements contain severe noise. A novel coupled dictionary learning technique is developed by including a suitable total-variation-based regularization term in the cost function. Furthermore, exploiting the smoothness of the datasets, new fast sparse coding algorithms are derived. The new techniques achieve effective modeling of the smooth signal and significantly alleviate the effects of noise. Finally, extensive simulation results for the problem of spectral super-resolution of hyperspectral images are provided, demonstrating the performance improvements offered by the derived techniques.