### Abstract

Language | English |
---|---|

Pages | 2510-2521 |

Number of pages | 12 |

Journal | Applied Sciences |

Volume | 8 |

Issue number | 12 |

DOIs | |

Status | Published - 6 Dec 2018 |

### Keywords

- underwater acoustics
- compressive sensing
- target scattering

### ASJC Scopus subject areas

- Acoustics and Ultrasonics
- Ocean Engineering

### Cite this

*Applied Sciences*,

*8*(12), 2510-2521. https://doi.org/10.3390/app8122510

**Construction of Measurement Matrix Based on Cyclic Direct Product and QR Decomposition for Sensing and Reconstruction of Underwater Echo.** / Sun, Tongjing; Cao, Hong; Blondel, Philippe; Guo, Yunfei; Shentu, Han.

Research output: Contribution to journal › Article

*Applied Sciences*, vol. 8, no. 12, pp. 2510-2521. https://doi.org/10.3390/app8122510

}

TY - JOUR

T1 - Construction of Measurement Matrix Based on Cyclic Direct Product and QR Decomposition for Sensing and Reconstruction of Underwater Echo

AU - Sun, Tongjing

AU - Cao, Hong

AU - Blondel, Philippe

AU - Guo, Yunfei

AU - Shentu, Han

N1 - Research output from the one-year visit to the University of Bath of Dr. Tongjing Sun, with funding from the Chinese Scholarship Council, to work with me.

PY - 2018/12/6

Y1 - 2018/12/6

N2 - Compressive sensing is a very attractive technique to detect weak signals in a noisy background, and to overcome limitations from traditional Nyquist sampling. A very important part of this approach is the measurement matrix and how it relates to hardware implementation. However, reconstruction accuracy, resistance to noise and construction time are still open challenges. To address these problems, we propose a measurement matrix based on a cyclic direct product and QR decomposition (the product of an orthogonal matrix Q and an upper triangular matrix R). Using the definition and properties of a direct product, a set of high-dimensional orthogonal column vectors is first established by a finite number of cyclic direct product operations on low-dimension orthogonal “seed” vectors, followed by QR decomposition to yield the orthogonal matrix, whose corresponding rows are selected to form the measurement matrix. We demonstrate this approach with simulations and field measurements of a scaled submarine in a freshwater lake, at frequencies of 40 kHz–80 kHz. The results clearly show the advantage of this method in terms of reconstruction accuracy, signal-to-noise ratio (SNR) enhancement, and construction time, by comparison with Gaussian matrix, Bernoulli matrix, partial Hadamard matrix and Toeplitz matrix. In particular, for weak signals with an SNR less than 0 dB, this method still achieves an SNR increase using less data.

AB - Compressive sensing is a very attractive technique to detect weak signals in a noisy background, and to overcome limitations from traditional Nyquist sampling. A very important part of this approach is the measurement matrix and how it relates to hardware implementation. However, reconstruction accuracy, resistance to noise and construction time are still open challenges. To address these problems, we propose a measurement matrix based on a cyclic direct product and QR decomposition (the product of an orthogonal matrix Q and an upper triangular matrix R). Using the definition and properties of a direct product, a set of high-dimensional orthogonal column vectors is first established by a finite number of cyclic direct product operations on low-dimension orthogonal “seed” vectors, followed by QR decomposition to yield the orthogonal matrix, whose corresponding rows are selected to form the measurement matrix. We demonstrate this approach with simulations and field measurements of a scaled submarine in a freshwater lake, at frequencies of 40 kHz–80 kHz. The results clearly show the advantage of this method in terms of reconstruction accuracy, signal-to-noise ratio (SNR) enhancement, and construction time, by comparison with Gaussian matrix, Bernoulli matrix, partial Hadamard matrix and Toeplitz matrix. In particular, for weak signals with an SNR less than 0 dB, this method still achieves an SNR increase using less data.

KW - underwater acoustics

KW - compressive sensing

KW - target scattering

U2 - 10.3390/app8122510

DO - 10.3390/app8122510

M3 - Article

VL - 8

SP - 2510

EP - 2521

JO - Applied Sciences

T2 - Applied Sciences

JF - Applied Sciences

SN - 2076-3417

IS - 12

ER -