  Compressive sensing (CS) has triggered enormous research activity since its
first appearance. CS exploits the signal's sparsity or compressibility in a
particular domain and integrates data compression and acquisition, thus
allowing exact reconstruction through relatively few non-adaptive linear
measurements. 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 which preserves the intrinsic structure of tensor data with reduced
computational complexity at reconstruction. GTCS offers an efficient means for
representation of multidimensional data by providing simultaneous acquisition
and compression from all tensor modes. In addition, we propound two
reconstruction procedures, a serial method (GTCS-S) and a parallelizable method
(GTCS-P). We then compare the performance of the proposed method with Kronecker
compressive sensing (KCS) and multi way compressive sensing (MWCS). We
demonstrate experimentally that GTCS outperforms KCS and MWCS in terms of both
reconstruction accuracy (within a range of compression ratios) and processing
speed. The major disadvantage of our methods (and of MWCS as well), is that the
compression ratios may be worse than that offered by KCS.
