IEICE Transactions on Communications
Online ISSN : 1745-1345
Print ISSN : 0916-8516
Regular Section
Sparse Random Block-Banded Toeplitz Matrix for Compressive Sensing
Xiao XUESong XIAOHongping GAN
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2019 Volume E102.B Issue 8 Pages 1565-1578


In compressive sensing theory (CS), the restricted isometry property (RIP) is commonly used for the measurement matrix to guarantee the reliable recovery of sparse signals from linear measurements. Although many works have indicated that random matrices with excellent recovery performance satisfy the RIP with high probability, Toeplitz-structured matrices arise naturally in real scenarios, such as applications of linear time-invariant systems. Thus, the corresponding measurement matrix can be modeled as a Toeplitz (partial) structured matrix instead of a completely random matrix. The structure characteristics introduce coherence and cause the performance degradation of the measurement matrix. To enhance the recovery performance of the Toeplitz structured measurement matrix in multichannel convolution source separation, an efficient construction of measurement matrix is presented, referred to as sparse random block-banded Toeplitz matrix (SRBT). The sparse signal is pre-randomized by locally scrambling its sample locations. Then, the signal is subsampled using the sparse random banded matrix. Finally, the mixing measurements are obtained. Based on the analysis of eigenvalues, the theoretical results indicate that the SRBT matrix satisfies the RIP with high probability. Simulation results show that the SRBT matrix almost matches the recovery performance of random matrices. Compared with the existing banded block Toeplitz matrix, SRBT significantly improves the probability of successful recovery. Additionally, SRBT has the advantages of low storage requirements and fast computation in reconstruction.

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© 2019 The Institute of Electronics, Information and Communication Engineers
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