Fast compressive sensing of high-dimensional signals with tree-structure sparsity pattern

Compressive sensing of multi-dimensional signals (tensors) only receives limited attention. Separable sensing and proper sparsity pattern play two key roles for compressive sensing of tensors to be feasible and efficient. In view of inherent characteristic of 2D images and 3D videos, we propose the use of tree-structure sparsity pattern in tensor compressive sensing and develop a multiway tree-structure sparsity pattern OMP algorithm in this paper. Experimental results demonstrate the effectiveness of our method in terms of recovery quality and speed.