Tensorial compressive sensing of jointly sparse matrices with applications to color imaging

摘要

The tasks of color and hyperspectral image reconstruction have been addressed in the context of Compressive Sensing (CS) frameworks in the past. Traditional CS methodologies exploit the underlying assumption that images are intrinsically sparse in some domain in order to reconstruct the image with few linear measurements, relative to its original dimensionality. Since the different color or spectral planes of such imagery are usually correlated, exploiting joint sparsity principles has been shown to be beneficial. Specifically, images reconstructed from a given number of measurements with so-called Multiple Measurement Vector (MMV) approaches have better fidelity relative to those yielded by Single Measurement Vector (SMV) frameworks which don't exploit joint sparsity constraints. Standard MMV approaches, however, operate by vectorizing the data, and effectively fail to preserve the intrinsic high-dimensional structure of the imagery. In this paper, we introduce a tensorial MMV approach that exploits joint sparsity constraints across both spatial dimensions of the images as opposed to only the rows or columns, as in traditional vectorial approaches, while still leveraging joint sparsity assumptions across the color or spectral planes. We demonstrate empirically that our method provides better reconstruction fidelity given a fixed number of measurements, and that it is also more computationally efficient.