2013/05/31 by Shmuel Friedland, Qun Li, Dan Schonfeld · 1 citation
Computer Science · Engineering · Mathematics · #Algorithm #Artificial intelligence #Compressed sensing #Compression (physics) #Computer science #Data compression #Geometry #Iterative reconstruction #Kronecker delta #Mathematics #Microwave Imaging and Scattering Analysis #Parallelizable manifold #Pattern recognition (psychology) #Physics #Representation (politics) #Signal processing #Signal reconstruction #Sparse and Compressive Sensing Techniques #Sparse approximation #Tensor (intrinsic definition) #Tensor decomposition and applications #cs.CV #cs.IT #math.IT #msc:15A69 #msc:65D18 #msc:68U05
paper · pdf · doi:10.1109/tip.2014.2348796
10 pages, 83 figures
openalex publication_date 2014/08/15 · arxiv created 2014/09/03 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Compressive sensing (CS) has triggered an 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 nonadaptive 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 multisensor 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 CS 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 and a parallelizable method. We then compare the performance of the proposed method with Kronecker compressive sensing (KCS) and multiway 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.