Generalized tensor compressive sensing

Compressive sensing (CS) has triggered enormous research activity since its first appearance. CS exploits the signal´s sparseness or compressibility in a particular domain and integrates data compression and acquisition. While conventional CS theory relies on data representation in the form of vectors, many data types in various applications such as color imaging, video sequences, and multi-sensor networks, are intrinsically represented by higher-order tensors. Application of CS to higher-order data representation is typically performed by conversion of the data to very long vectors that must be measured using very large sampling matrices, thus imposing a huge computational and memory burden. In this paper, we propose Generalized Tensor Compressive Sensing (GTCS)- a unified framework for compressive sensing of higher-order tensors. GTCS offers an efficient means for representation of multidimensional data by providing simultaneous acquisition and compression from all tensor modes. In addition, we compare the performance of the proposed method with Kronecker compressive sensing (KCS). We demonstrate experimentally that GTCS outperforms KCS in terms of both accuracy and speed.