Strategy for Accelerating Multiway Greedy Compressive Sensing Reconstruction

The multiway greedy algorithm is widely used for reconstructions of Tucker-decomposition-based compressive sensing. However, its practicability is limited by the fact that only one support can be updated in most iterations, which increases the required number of iterations and influences the reconstruction speed. To address this problem, in this letter, we propose a strategy for accelerating the multiway greedy reconstruction. The proposed strategy allows all supports to be updated in an iteration such that an over-estimated greedy solution can be obtained through only a few iterations, and the superfluous indexes of each support are removed in subsequent iterations. The computational complexity of the proposed strategy is significantly reduced, comparing to that of the standard multiway greedy algorithm. Simulation results demonstrate that the proposed strategy can expedite the multiway greedy reconstruction without loss of accuracy.