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Chin. Phys. B, 2026, Vol. 35(5): 054301    DOI: 10.1088/1674-1056/ae118d
ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS Prev   Next  

Optimized iterative shrinkage threshold generalized inverse beamforming for sound source localization

Huihui He(何辉辉)3, Xinyu Wang(王欣宇)3, Zeyu Yang(杨泽宇)3, Xiaofei Wu(吴晓飞)4, and Shengguo Shi(时胜国)1,2,3,†
1 National Key Laboratory of Underwater Acoustic Technology, Harbin Engineering University, Harbin 150001, China;
2 Key Laboratory of Marine Information Acquisition and Security (Harbin Engineering University), Ministry of Industry and Information Technology, Harbin 150001, China;
3 College of Underwater Acoustic Engineering, Harbin Engineering University, Harbin 150001, China;
4 China Ship Scientific Research Center, Wuxi 214082, China
Abstract  This work addresses underwater noise source localization. Leveraging the spatial sparsity of sound sources, we employ an optimized iterative shrinkage-thresholding generalized inverse beamforming (OISTA-GIB) method to localize noise sources. Firstly, the sparsity of sound sources is exploited by introducing the $\lambda_{1}$ norm, resulting in an objective function that combines the $\lambda_{1}$ norm, with generalized inverse beamforming. This function is solved using an iterative shrinkage-thresholding algorithm (ISTA) to obtain sound source positions. Secondly, we note that when ISTA solves this objective function, the penalty strength applied by the identity matrix to all scanning points on the sound source surface is uniform. This uniformity reduces positioning accuracy. To enhance localization accuracy and spatial resolution, we propose an iterative regularization matrix-optimized ISTA to solve the objective function. Here, the result from the previous iteration is used to construct a regularization matrix that increases the penalty strength in non-source regions during the current iteration. This process iteratively narrows the mainlobe width in source regions until termination conditions are met, yielding refined sound source positions. Finally, simulations and experimental data processing show that the proposed OISTA-GIB method achieves higher accuracy and spatial resolution in noise source localization compared to existing methods.
Keywords:  generalized inverse beamforming      iterative regularization matrix      iterative shrinkage threshold      fast iterative shrinkage threshold  
Received:  12 July 2025      Revised:  26 September 2025      Accepted manuscript online:  10 October 2025
PACS:  43.60.+d (Acoustic signal processing)  
  43.58.+z (Acoustical measurements and instrumentation)  
  43.50.+y (Noise: its effects and control)  
Fund: Project supported by the National Key Scientific Instrument and Equipment Development Projects of China (Grant No. 52327901).
Corresponding Authors:  Shengguo Shi     E-mail:  shishengguo@hrbeu.edu.cn

Cite this article: 

Huihui He(何辉辉), Xinyu Wang(王欣宇), Zeyu Yang(杨泽宇), Xiaofei Wu(吴晓飞), and Shengguo Shi(时胜国) Optimized iterative shrinkage threshold generalized inverse beamforming for sound source localization 2026 Chin. Phys. B 35 054301

[1] Gao Y, Yang B Q and Shi S G 2023 Chin. Phys. B 32 044302
[2] Zhang H Y, Li F Q, Wang P, Xin W and Liu Y Z 2025 The Journal of the Acoustical Society of America 157 3402
[3] Yue Y X, Zhang Z Y and Shi Z G 2024 IEEE Transactions on Aerospace and Electronic Systems 60 5663
[4] Jiang S Y, Jiang R X, Liu X S, Gu B X and Chen Y W 2024 IEEE Journal of Oceanic Engineering 49 340
[5] Zhao D D, Chen P, Hu Y T, Liang R H, Wang H X and Guo X X 2021 IEEE Journal of Oceanic Engineering 46 1356
[6] Firat U and Akgül T 2024 Signal Processing 214 109221
[7] Yu Y C, Shi P C, Krynkin A and Horoshenkov K V 2024 Measurement 238 115361
[8] Suzuki T 2011 Journal of Sound and Vibration 330 5835
[9] Guo X, Wu X, Liu X Q and Tang L J 2023 Journal of Mechanical Science and Technology 37 43
[10] Shi S G, Gao Y, Yang D S, Shi J and Tian D Y 2021 IEEE Sensors Journal 21 16222
[11] Zamponi R, Chiariotti P, Battista G, Schram C and Castellini P 2020 Applied Acoustics 163 107229
[12] Merino-Martínez R, Salil Luesutthiviboon S, Zamponi R, Alejandro Rubio C A, Ragni D, Sijtsma P, Snellen M and Schram C 2020 Journal of Sound and Vibration 470 115176
[13] Wu Y X, Zhang H C K, Kang J and Boctor E M 2020 Ultrasonics 103 106098
[14] Zhang Z F, Chen S, Xu Z M, He Y S and Li S 2017 Journal of Sound and Vibration 396 108
[15] Li W, S. Zhao S, Zhou C, Qin Y M, Zhu H R and Li S L 2025 Measurement 242 116238
[16] Presezniak F, Zavala P A G, Steenackers G, Janssens K, Arruda J R F, Desmet W and Guillaume P 2012 Mechanical Systems and Signal Processing 32 349
[17] Zavala P A G, RoeckWD, Janssens K, Arruda J R F, Sas P and Desmet W 2011 Mechanical Systems and Signal Processing 25 928
[18] Daubechies I, Defrise M and Mol C D 2004 Communications on Pure and Applied Mathematics 57 1413
[19] Bredies K 2009 Journal of Inverse and Ill-Posed Problems 17 19
[20] Wang Q, Meng C, Ma W N, Wang C and Yu L 2019 Measurement 142 68
[21] Shen L B, Chu Z G, Zhang Y X and Yang Y 2020 Journal of Low Frequency Noise Vibration and Active Control 39 866
[22] Hu M S, Zheng G Q, Su Z, Kong L R and Wang G D 2024 Energy 303 131951
[23] Liu S M, Chen H W, Liu P X, Qin F Z and Fars A 2023 International Journal of Hydrogen Energy 48 34486
[24] Ghazali S M and Baleghi Y 2023 Knowledge-Based Systems 275 110683
[25] Karmarkar N 1984 Combinatorica 4 373
[26] Malyuta D, Reynolds T P, Szmuk M, Lew T, Bonalli R and Pavone M 2022 IEEE Control Systems Magazine 42 40
[27] Zhou X W, Liu F T, Yin Z Y, Jin Y F and Zhang C B 2022 Computers and Geotechnics 145 104701
[28] Li J, Li X R and Zhao L Y 2017 International Journal of Wavelets Multiresolution and Information Processing 15 1750059
[29] Dokuz Y and Tüfekci Z 2022 Multimedia Tools and Applications 81 9969
[30] Zheng P C, Lyu X T and Gong Y 2023 IEEE Wireless Communications Letters 12 1781
[31] Liu Q, Chu N, Yu L, Ning Y and Wu P 2022 IEEE Transactions on Instrumentation and Measurement 71 6501612
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