在聲學成像與定位領域中，空間解析度與動態範圍為評估演算法性能之核心指標。傳統波束成形 (Conventional Beamforming, CB) 因計算穩定且實作簡單，長期作為聲學成像之基準方法。然而，其空間解析度受瑞利準則限制，主瓣寬度與波長成正比，在低頻或有限孔徑條件下，難以分離距離相近聲源且動態範圍受限。本研究系統性比較 DAS 與三種去卷積方法 (CLEAN-PSF、CLEAN-SC、HR-CLEAN-SC) 於近距離多聲源條件下之聲學成像表現，並以空間解析度、峰值分離能力與動態範圍作為評估指標。CLEAN-PSF 透過理論點擴散函數 (Point Spread Function, PSF) 之迭代減法程序逐步移除主峰及其旁瓣，可有效提升空間解析度並恢復圖像清晰，缺點是當聲源具有延展性或相干性時，易產生陣幅估計偏差。CLEAN-SC 透過估計與主峰位置相關之聲源分量，直接對交叉譜矩陣進行去卷積，其過程具備較佳的物理一致性，然而在極近距離多聲源情境下，因 PSF 主瓣重疊，仍可能受到鄰近聲源干擾而限制其聲源分離能力。HR-CLEAN-SC 於點擴散函數主瓣範圍內選取干擾最小之替代標記點以估計聲源分量，使其更接近真實聲源分布，進而降低多源互擾並提升峰值銳利度與動態範圍。結果顯示，HR-CLEAN-SC 在主瓣重疊情況下能有效分離相鄰聲源，其峰值清晰度與動態範圍均顯著優於傳統方法，驗證其具備高解析度聲學成像性能與複雜聲場定位應用之潛力。

This thesis investigates the localization of closely spaced multiple noise sources by comparing conventional beamforming (CB), CLEAN-PSF, CLEAN-SC, and High-Resolution CLEAN-SC (HR-CLEAN-SC). Although CB is computationally stable and easy to implement, its spatial resolution is constrained by the Rayleigh criterion. At low frequencies or with a limited array aperture, the point spread functions of adjacent sources overlap significantly, causing multiple sources to merge into a broad energy region and reducing both localization accuracy and dynamic range. CLEAN-PSF improves image concentration by iteratively removing the dominant peak and its theoretical point spread function, but it may produce residual peaks, false sources, or inaccurate energy estimates when the theoretical model does not match the measured sound field or when several source main lobes strongly overlap. CLEAN-SC instead extracts spatially coherent source components directly from the cross-spectral matrix, resulting in cleaner acoustic maps and improved physical consistency. However, when source spacing is below the conventional resolution limit, the selected beamforming peak may be influenced by multiple neighboring sources, causing the estimated source response vector to contain mixed contributions. HR-CLEAN-SC addresses this limitation by searching within the main-lobe region for an alternative marker position that is less affected by neighboring sources and then using this position to estimate and remove each source component. Numerical simulations were performed using a 96-microphone array with two, three, and four incoherent point sources separated by 0.25 m over a range of frequencies. The results showed that HR-CLEAN-SC produced sharper source peaks, separated adjacent sources at lower frequencies, and yielded more stable sound-pressure-level estimates that were closer to single-source reference values. Semi-anechoic experiments using two- and three-speaker configurations further confirmed these trends. Overall, HR-CLEAN-SC improved localization stability and spatial resolution without changing the array hardware. Under the two-source simulation conditions, its minimum resolvable frequency was approximately half that of conventional CLEAN-SC, corresponding to nearly twice the spatial resolution, although its advantage gradually decreased as the number of sources and mutual interference increased.

[1] Paolo Chiariotti, Milena Martarelli, and Paolo Castellini. Acoustic beamforming for noise source localization – Reviews, methodology and applications. Mechanical Systems and Signal Processing, 120:422–448, 2019.
[2] Leandro de Santana. Fundamentals of acoustic beamforming. Technical report, NATO Science and Technology Organization, 2017.
[3] Pieter Sijtsma. CLEAN based on spatial source coherence. International Journal of Aeroacoustics, 6(4):357–374, 2007.
[4] Pieter Sijtsma, Roberto Merino-Martinez, Anwar MN Malgoezar, and Mirjam Snellen.High-resolution CLEAN-SC: Theory and experimental validation. International Journal of Aeroacoustics, 16(4-5):274–298, 2017.
[5] Roberto Merino Martinez. Microphone arrays for imaging of aerospace noise sources.Phd dissertation, Delft University of Technology, 2018.
[6] T. Padois, J. Fischer, C. Doolan, and O. Doutres. Acoustic Imaging with Conventional Frequency Domain Beamforming and Generalized Cross Correlation: A Comparison Study. Applied Acoustics, 177:107914, 2021.
[7] Y. Wang, Z. Deng, J. Zhao, V. F. Kopiev, D. Gao, and W.-L. Chen. Progress in Beamforming Acoustic Imaging Based on Phased Microphone Arrays: Algorithms and Applications. Measurement, 242:116100, 2025
[8] S. L. Hahn and S. A. Tretter. Minimum-variance distortionless response beamforming of acoustic signals. The Journal of the Acoustical Society of America, 104(2):947–956,1998.
[9] Ralph O. Schmidt. Multiple emitter location and signal parameter estimation. IEEE Transactions on Antennas and Propagation, 34(3):276–280, March 1986.
[10] Thomas F. Brooks and William M. Humphreys. A deconvolution approach for the mapping of acoustic sources (damas) determined from phased microphone arrays. In 10th AIAA/CEAS Aeroacoustics Conference, number AIAA-2004-2954, Manchester, United Kingdom, 2004.
[11] Ennes Sarradj. A fast signal subspace approach for the determination of absolute levels from phased microphone array measurements. Journal of Sound and Vibration,329(9):1553–1569, 2010.
[12] Takao Suzuki. 𝑙1 generalized inverse beam-forming algorithm resolving coherent/incoherent, distributed and multipole sources. Journal of Sound and Vibration,330(24):5835–5851, 2011.
[13] Y. Yang, Z. Chu, and S. Yin. Two-Dimensional Grid-Free Compressive Beamforming with Spherical Microphone Arrays. Mechanical Systems and Signal Processing,169:108642, 2022.
[14] Jérôme Antoni. A bayesian approach to sound source reconstruction: Optimal basis, regularization, and focusing. The Journal of the Acoustical Society of America,131(4):2873–2890, 2012
[15] N. Chu, Y. Ning, L. Yu, Q. Huang, and D. Wu. A high-resolution and low-frequency acoustic beamforming based on bayesian inference and nonsynchronous measurements. IEEE Access, 8:82500–82513, 2020.
[16] Robert P. Dougherty. Functional beamforming for aeroacoustic source distributions. In 20th AIAA/CEAS Aeroacoustics Conference, number AIAA-2014-3066, 2014.
[17] R. Merino-Martinez, C. VanDercreek, and M. Snellen. Evaluation of Advanced Acoustic Imaging Methods for Microphone-Array Measurements in Closed-Section Wind Tunnels. In 28th AIAA/CEAS Aeroacoustics Conference, 2022. AIAA Paper 2022-2810.
[18] A. Kujawski and E. Sarradj. Fast Grid-Free Strength Mapping of Multiple Sound Sources from Microphone Array Data Using a Transformer Architecture. The Jounal of the Acoustical Society of America, 152(5):2543–2556, 2022.
[19] Martinus Petrus Johannes Sanders. Study on the Application of Digital MEMS Microphones for Aeroacoustic Noise Source Localization for Large Drones. Thesis, University of Twente, January 2017. https://www.researchgate.net/publication/315671125.
[20] L. Yu, J. Antoni, J. Deng, C. Li, and W. Jiang. Low-Rank Gaussian Mixture Modeling of Space-Snapshot Representation of Microphone Array Measurements for Acoustic Imaging in a Complex Noisy Environment. Mechanical Systems and Signal Processing,165:108294, 2022.
[21] Y. Li, M. Li, D. Feng, W. Pan, L. Wei, and D. Yang. Low-Frequency Acoustic Source Localization Based on the Cross-Spectral Time Reversal Method Corrected in Wavenumber Domain. Measurement, 188:110579, 2022.
[22] Jørgen Grythe. Evaluating array resolution. Technical note, Norsonic AS, Oslo, Norway,2015. Revised August 27, 2015.
[23] Zebb Prime and Con Doolan. A comparison of popular beamforming arrays. In Proceedings of ACOUSTICS 2013, Victor Harbor, Australia, November 2013.
[24] Christof Ocker and Wolfram Pannert. Calculation of the cross spectral matrix with Daniell’s method and application to acoustical beamforming. Applied Acoustics,120:59–69, 2017.
[25] T. Lobato, R. Sottek, and M. Vorländer. Deconvolution with Neural Grid Compression:A Method to Accurately and Quickly Process Beamforming Results. The Journal of the Acoustical Society of America, 153(4):2073–2089, 2023.