Computationally Efficient and Secure Kronecker-based Compressive Sensing

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  • We propose an efficient permuted Kronecker-based sparse measurement matrix for compressive sensing applications. We use sub-matrices to create a block-diagonal matrix and multiply it with a deterministic permutation matrix to measure the sparse or compressible signals. Using ECG signals from the MIT-BIH Arrhythmia database, we show that the reconstructed signal quality is comparable to the ones achieved using standard compressive sensing methods. Our methodology results in an overall reduction in storage and computations and can be generalized to other classes of eligible measurement matrices in compressive sensing. We show that with the use of a securely generated one-time sensing matrix, our proposed method is computationally secure against plaintext and ciphertext-only attacks. The proposed one-time sensing matrix is superior to other measurement matrices in the literature in terms of the number of linear feedback shift register bits required for their generation.

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  • Copyright © 2021 the author(s). Theses may be used for non-commercial research, educational, or related academic purposes only. Such uses include personal study, research, scholarship, and teaching. Theses may only be shared by linking to Carleton University Institutional Repository and no part may be used without proper attribution to the author. No part may be used for commercial purposes directly or indirectly via a for-profit platform; no adaptation or derivative works are permitted without consent from the copyright owner.
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  • 2021


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