The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Dalam teori penderiaan mampatan (CS), sifat isometri terhad (RIP) biasanya digunakan untuk matriks pengukuran untuk menjamin pemulihan isyarat jarang yang boleh dipercayai daripada pengukuran linear. Walaupun banyak kerja telah menunjukkan bahawa matriks rawak dengan prestasi pemulihan yang sangat baik memenuhi RIP dengan kebarangkalian yang tinggi, matriks berstruktur Toeplitz timbul secara semula jadi dalam senario sebenar, seperti aplikasi sistem invarian masa linear. Oleh itu, matriks ukuran yang sepadan boleh dimodelkan sebagai matriks berstruktur Toeplitz (separa) dan bukannya matriks rawak sepenuhnya. Ciri-ciri struktur memperkenalkan keselarasan dan menyebabkan kemerosotan prestasi matriks pengukuran. Untuk meningkatkan prestasi pemulihan matriks pengukuran berstruktur Toeplitz dalam pemisahan sumber lilitan berbilang saluran, pembinaan matriks pengukuran yang cekap dibentangkan, dirujuk sebagai matriks Toeplitz jalur rawak rawak jarang (SRBT). Isyarat jarang dipra-rawak dengan mengacak lokasi sampelnya secara tempatan. Kemudian, isyarat disubsampel menggunakan matriks jalur rawak jarang. Akhirnya, ukuran pencampuran diperolehi. Berdasarkan analisis nilai eigen, keputusan teori menunjukkan bahawa matriks SRBT memenuhi RIP dengan kebarangkalian yang tinggi. Keputusan simulasi menunjukkan bahawa matriks SRBT hampir sepadan dengan prestasi pemulihan matriks rawak. Berbanding dengan matriks Toeplitz blok berjalur sedia ada, SRBT meningkatkan dengan ketara kebarangkalian pemulihan yang berjaya. Selain itu, SRBT mempunyai kelebihan keperluan penyimpanan yang rendah dan pengiraan pantas dalam pembinaan semula.
Xiao XUE
Xidian University
Song XIAO
Xidian University
Hongping GAN
Xidian University
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Salinan
Xiao XUE, Song XIAO, Hongping GAN, "Sparse Random Block-Banded Toeplitz Matrix for Compressive Sensing" in IEICE TRANSACTIONS on Communications,
vol. E102-B, no. 8, pp. 1565-1578, August 2019, doi: 10.1587/transcom.2018EBP3247.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/communications/10.1587/transcom.2018EBP3247/_p
Salinan
@ARTICLE{e102-b_8_1565,
author={Xiao XUE, Song XIAO, Hongping GAN, },
journal={IEICE TRANSACTIONS on Communications},
title={Sparse Random Block-Banded Toeplitz Matrix for Compressive Sensing},
year={2019},
volume={E102-B},
number={8},
pages={1565-1578},
abstract={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.},
keywords={},
doi={10.1587/transcom.2018EBP3247},
ISSN={1745-1345},
month={August},}
Salinan
TY - JOUR
TI - Sparse Random Block-Banded Toeplitz Matrix for Compressive Sensing
T2 - IEICE TRANSACTIONS on Communications
SP - 1565
EP - 1578
AU - Xiao XUE
AU - Song XIAO
AU - Hongping GAN
PY - 2019
DO - 10.1587/transcom.2018EBP3247
JO - IEICE TRANSACTIONS on Communications
SN - 1745-1345
VL - E102-B
IS - 8
JA - IEICE TRANSACTIONS on Communications
Y1 - August 2019
AB - 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.
ER -