Improvement of non-negative matrix factorization-based active sonar reverberation suppression method using L1-norm and majorization-minimization

Seokjin Lee; Wonnyoung Lee; Yena You; Seungheon Lee; Daekyung Kim; Junsub Nam

doi:10.7776/ASK.2025.44.2.094

All Issue

2025 Vol.44, Issue 2 Preview Page Next Page

Research Article

Improvement of non-negative matrix factorization-based active sonar reverberation suppression method using L1-norm and majorization-minimization L1-노름과 주요화최소화 기법을 활용한 비음수 행렬 분해 기반 능동소나 잔향제거 개선 방법

31 March 2025. pp. 94-108

PDF XML

Abstract

In this paper, we conduct research on an algorithm to suppress reverberation using a non-negative matrix factorization technique for target detection using an active sonar system. In this paper, we focus on the disadvantage that conventional algorithm estimates the target echo and reverberation bases through iterative estimation, which takes a long time to calculate. To improve this, we use the L1-norm to quickly converge to the desired solution at the beginning of the iteration. In addition, considering the fact that the heuristic multiplicative update method used in the conventional algorithm does not mathematically guarantee the convergence of additional penalty functions, the update equation is developed through a majorization-minimization technique that can guarantee convergence. Simulations were performed to verify the algorithm, and the results showed that the signal-to-noise ratio performance of the proposed algorithm was improved by 3 dB compared to the conventional algorithm.

Keywords

Active sonar

Reverberation suppression

Non-negative matrix factorization

Majorization-minimization

본 논문에서는 능동 소나 시스템을 이용한 표적 탐지를 위해 비음수 행렬 분해 기법을 활용하여 잔향을 제거하는 기법에 대한 연구를 진행하였다. 본 논문에서는 기존의 기법이 반복 추정을 통해 표적 및 잔향 기저를 추정하여 연산 시간이 오래 걸린다는 단점에 주목하였다. 이를 개선하기 위하여 L1-노름을 활용하여 반복 초기에 원하는 해로 빠르게 수렴할 수 있도록 하였다. 또한, 기존의 기법이 활용하고 있는 휴리스틱 곱셈 갱신 기법은 추가적인 비용 함수를 활용할 경우 수학적으로 수렴을 보장하지 못하기 때문에, 수렴을 보장할 수 있는 주요화최소화 기법을 통해 갱신식을 새롭게 도출하였다. 본 알고리즘을 검증하기 위하여 시뮬레이션을 수행하였으며, 제안하는 알고리즘이 기존 대비 약 3 dB 향상된 신호대잔향비 성능을 보였다.

키워드

능동 소나

잔향 제거

비음수 행렬 분해

주요화최소화

References

L. E. Kinsler, A. R. Frey, A. B. Coppens, and J. V. Sanders, Fundamentals of Acoustics, 4th ed (John Wiley & Sons, Hoboken, 2000), pp. 456-464.

T. Collins and P. Atkins, "Doppler-sensitive active sonar pulse designs for reverberation processing," IEE Proc. Radar Sonar Navig. 145, 347-353 (1998).

10.1049/ip-rsn:19982434

S. Ward, "The use of sinusoidal frequency modulated pulses for low Doppler detection," Proc. IEEE Oceans, 2147-2151 (2001).

10.1109/OCEANS.2001.968331

G. Kim, K. Lee, K. Yoon, and S. Lee, "A study on pulse train waveforms for high duty cycle sonar systems: optimization scheme and relationship between orthogonality and bandwidth," IEEE Access, 9, 119800-119817 (2021).

10.1109/ACCESS.2021.3107907

S. Kay and J. Salisbury, "Improved active sonar detection using autoregressive preshiteners," J. Acoust. Soc. Am. 87, 1603-1611 (1990).

10.1121/1.399408

G. Ginolhac and G. Jourdain, "Principal component inverse algorihtm for detection in the presence of reverberation," IEEE J. Oean. Eng. 27, 310-321 (2002).

10.1109/JOE.2002.1002486

W. Li, Q. Zhang, X. Ma, and C. Hou, "Active sonar detection in reverberation via signal subspace extraction algorithm," EURASIP J. Wirel. Commun. Netw. 2010, 1-10 (2010).

10.1155/2010/981045

D. D. Lee and H. S. Seung, "Learning the parts of objects by non-negative matrix factorization," Nature, 401, 788-791 (1999).

10.1038/4456510548103

D. D. Lee and H. S. Seung, "Algorithms for non-negative matrix factorization," Proc. NeurIPS, 556-562 (2001).

P. Smaragdis and J. C. Brown, "Non-negative matrix factorization for polyphonic music transcription," Proc. IEEE WASPAA, 177-180 (2003).

10.1109/ASPAA.2003.1285860

M. Sun, Y. Li, J. F. Gemmeke, and X. Zhang, "Speech enhancement under low SNR conditions via noise estimation using sparse and low-rank NMF with Kullback-Leibler divergence," IEEE/ACM Trans. Audio. Speech. Lang. Process. 23, 1233-1242 (2015).

10.1109/TASLP.2015.2427520

S. Lee and J.-S. Lim, "Reverberation suppression using non-negative matrix factorization to detect low-doppler target with continuous wave active sonar," EURASIP J. Adv. Signal Process. 2019, 1-18 (2019).

10.1186/s13634-019-0608-6

G. Kim, K. Lee, and S. Lee, "Linear frequency modulated reverberation suppression using non-negative matrix factorization methods, dechirping trasnformation, and modulo operation," IEEE Access, 8, 110720-110737 (2020).

10.1109/ACCESS.2020.3001865

A. Marmin, J. H. de Morais Goulart, and C. Fevotte, "Majorization-minimization for sparse nonnegative matrix factorization with the beta-divergence," IEEE Trans. Signal. Process. 71, 1435-1447 (2023).

10.1109/TSP.2023.3266939

S. Lee and G. Kim, "A Study on the active sonar reverberation suppression method based on non-negative matrix factorization with beta-divergence function" (in Korean), J. Acoust. Soc. Kr. 43, 369-382 (2024).

D. A. Abaham and A. P. Lyons, "Simulation of non-rayleigh reverberation and clutter," IEEE J. Oceanic Eng. 29, 347-362 (2004).

10.1109/JOE.2004.828202

Information

Publisher :The Acoustical Society of Korea
Publisher(Ko) :한국음향학회
Journal Title :The Journal of the Acoustical Society of Korea
Journal Title(Ko) :한국음향학회지
Volume : 44
No :2
Pages :94-108
Received Date : 2024-12-17
Revised Date : 2025-02-11
Accepted Date : 2025-02-11
DOI :https://doi.org/10.7776/ASK.2025.44.2.094

The Journal of the Acoustical Society of KoreaISSN:1225-4428(Print) 2287-3775(Online)한국음향학회

All Issue