The Dictionary Learning Algorithm Of Tensors Compressed Sensing And Applications

The main target of this paper is to study tensor compressed sensing algorithm of multidimensional signal,the emphasis is a dictionary learning algorithm based on high-order singular value decomposition and its application in video signals.Tensor Compressed Sensing(Tensor Compressed Sensing)is a new method of dealing with multidimensional data in recent years,such as video sequence,medical imaging and hyperspectral image.One of the inherent limitations of traditional compressed sensing theory is that it can only represent data sparsely in the form of a vector.For multidimensional signals,if the original signal is vectorized,not only is it easy to destroy certain structural information of the signal itself,but also the computational complexity is greatly increased in the optimization process,thereby reducing the efficiency of signal reconstruction.But when multidimensional signals are represented as tensors,processing multidimensional signals in the form of tensors allows the structure of the data to be preserved.Therefore,how to extend the traditional theory of compressive sensing to tensor compression is the focus of our research.In this paper,a HOSVDDL algorithm(Higher Order SVD Dictionary Learning)is proposed for the video sequences.Based on the Tucker decomposition model,the core tensor is used as the sparse representation coefficient,and each factor is used as a dictionary.Under the premise of ensuring the sparsity,the dictionary is optimized and the tensor data are fully approximated.Compared with the existing Kronecker Dictionary Learning algorithm,the proposed method shows superiority in representing error and peak signal-to-noise ratio(PSNR).