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Compressive sensing of sparse tensors.

Shmuel Friedland, Qun Li, Dan Schonfeld

    IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
    |August 20, 2014
    PubMed
    Summary

    Generalized tensor compressive sensing (GTCS) offers efficient multidimensional data acquisition and compression. GTCS outperforms existing methods in reconstruction accuracy and speed for higher order tensors.

    Area of Science:

    • Signal Processing
    • Data Science
    • Applied Mathematics

    Background:

    • Compressive Sensing (CS) theory traditionally relies on vector data representations.
    • Higher order tensors are common in applications like color imaging and video sequences.
    • Vectorizing tensor data for CS leads to significant computational and memory burdens.

    Purpose of the Study:

    • To introduce Generalized Tensor Compressive Sensing (GTCS), a unified framework for CS of higher order tensors.
    • To preserve the intrinsic tensor structure for reduced reconstruction complexity.
    • To enable simultaneous acquisition and compression across all tensor modes.

    Main Methods:

    • Developed GTCS, a novel framework for multidimensional tensor data.
    • Proposed two reconstruction algorithms: a serial method and a parallelizable method.

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  • Compared GTCS performance against Kronecker Compressive Sensing (KCS) and Multiway Compressive Sensing (MWCS).

    • Main Results:

    • GTCS demonstrated superior reconstruction accuracy compared to KCS and MWCS within tested compression ratios.
    • GTCS achieved faster processing speeds than KCS and MWCS.
    • The primary limitation identified is potentially lower compression ratios compared to KCS.

    Conclusions:

    • GTCS provides an efficient and accurate method for compressive sensing of higher order tensor data.
    • The proposed framework reduces computational complexity and improves processing speed.
    • GTCS represents a significant advancement for multidimensional signal acquisition and compression.