Spatio-spectral data reconstruction in terahertz imaging

The problem of multidimensional data reconstruction from an incomplete set of observations is addressed in this paper. It has been recently shown that learned dictionaries are very effective in image denoising and inpainting applications. Here we extend the core idea in image inpainting to the case of 3-D data. Our main objective is to exploit both spatial and spectral/temporal information for recovering the missing samples. We show that this approach has superiority over the case where one treats the spectral/temporal images independently. We first propose to learn a spatio-spectral/temporal dictionary from a subset of available training data. Using this dictionary, we then jointly recover the original data samples from an incomplete set of observations. Our experimental results confirm significant improvement over the existing methods.