Compressive Tensor Sampling with Structured Sparsity
Conventional Compressive Sensing (CS) obscures the intrinsic structures of multidimensional signals with the vectorized representation. Although tensor-based CS methods can preserve the intrinsic multidimensional structures with reduced computational complexity, their sampling efficiency and recovery performance are degraded with the assumption of standard/simple sparsity. This paper proposes a general and adaptive model that incorporates structured sparsity into tensor representation to fit the varying nonstationary statistics of multidimensional signals. To guarantee the block sparsity, subspace clustering is adopted to adaptively generate the union of tensor subspaces with its basis of each tensor subspace learned for optimized representation. For sampled tensors, the stable recovery algorithm is developed to achieve desirable recovery performance using fewer degrees of freedom. Moreover, the proposed model inherits the merit from tensor-based CS to alleviate the computational and storage burden in sampling and recovery. Experimental results demonstrate that the proposed model can achieve better recovery performance in video sampling in comparison to the state-of-the-art tensor-based method.