Selective Locking Tensor Orthogonal Matching Pursuit algorithm based on block sparsity for multidimensional compressive sensing

Greedy algorithms for multidimensional compressive sensing (CS) faces heavy computational complexity. In this paper, we develop a new greedy algorithm based on multidimensional block sparsity model, namely Selective Locking Tensor Orthogonal Matching Pursuit algorithm (SLTOMP). Comparing with traditional tensor greedy algorithm, the proposed algorithm is able to judge that whether the current index of atom is more valuable for searching than others, and then decide whether or not to lock the current index to avoid finding it again during the following iterations. We repeat the 'judge and lock' step for each dimension during an iteration, in order to reduce the redundant selection of atoms. As a result, we improve the reconstruction speed without a compromise of accuracy, which is verified by the simulations of synthetic block-sparse data and hyperspectral image data.