TenSR: Multi-dimensional Tensor Sparse Representation

The conventional sparse model relies on data representation in the form of vectors. It represents the vector-valued or vectorized one dimensional (1D) version of an signal as a highly sparse linear combination of basis atoms from a large dictionary. The 1D modeling, though simple, ignores the inherent structure and breaks the local correlation inside multidimensional (MD) signals. It also dramatically increases the demand of memory as well as computational resources especially when dealing with high dimensional signals. In this paper, we propose a new sparse model TenSR based on tensor for MD data representation along with the corresponding MD sparse coding and MD dictionary learning algorithms. The proposed TenSR model is able to well approximate the structure in each mode inherent in MD signals with a series of adaptive separable structure dictionaries via dictionary learning. The proposed MD sparse coding algorithm by proximal method further reduces the computational cost significantly. Experimental results with real world MD signals, i.e. 3D Multi-spectral images, show the proposed TenSR greatly reduces both the computational and memory costs with competitive performance in comparison with the state-of-the-art sparse representation methods. We believe our proposed TenSR model is a promising way to empower the sparse representation especially for large scale high order signals.