Adaptive Sparse Representation for Kronecker Compressive Sensing

Kronecker compressive sensing (KCS) technique is used for compressively sampling multi-dimensional signals, and reconstructing them from their measurements. In order to obtain more accurate reconstruction, the learned dictionaries are usually employed for Tucker-decomposition-based sparse representation of original signals. Such dictionaries are learned in advance by using a set of multi-dimensional training samples which contain similar structures with the original signals. However, the prior information of the original signals may be unknown in advance. In such case, it is infeasible to select proper samples for dictionary learning. To overcome this limitation, in this paper, we propose an adaptive approach for sparse representation of KCS. The proposed approach achieves dynamic update of dictionaries without requiring the prior information of original signals. As a result, the reconstruction accuracy can be continually improved as the number of input signals increases, which is verified through the simulations on real images.