An Algorithm for Parallel Reconstruction of Jointly Sparse Tensors with Applications to Hyperspectral Imaging

A wide range of Compressive Sensing (CS) frameworks have been proposed to address the task of color and hyperspectral image sampling and reconstruction. Methods for reconstruction of jointly sparse vectors that leverage joint sparsity constraints such as the Multiple Measurement Vector (MMV) approach have been shown to outperform Single Measurement Vector (SMV) frameworks. Recent work has shown that exploiting joint sparsity while simultaneously preserving the high-dimensional structure of the data results in further performance improvements. We introduce a parallelizable extension of a previously proposed serial tensorial MMV approach which, like its predecessor, exploits joint sparsity constraints multiple data dimensions simultaneously, but that is parallelizable in nature. We demonstrate empirically that the proposed method provides better reconstruction fidelity of hyperspectral imagery and that it is also more computationally efficient than the current state of the art.