{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:01:15Z","timestamp":1760144475974,"version":"build-2065373602"},"reference-count":52,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,4,24]],"date-time":"2024-04-24T00:00:00Z","timestamp":1713916800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62071419"],"award-info":[{"award-number":["62071419"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Ocean Acoustic Waveguide Remote Sensing (OAWRS) typically utilizes large-aperture linear arrays combined with coherent beamforming to estimate the spatial distribution of acoustic scattering echoes. The conventional maximum likelihood deconvolution (DCV) method uses a likelihood model that is inaccurate in the presence of multiple adjacent targets with significant intensity differences. In this study, we propose a deconvolution algorithm based on a modified likelihood model of beamformed intensities (M-DCV) for estimation of the spatial intensity distribution. The simulated annealing iterative scheme is used to obtain the maximum likelihood estimation. An approximate expression based on the generalized negative binomial (GNB) distribution is introduced to calculate the conditional probability distribution of the beamformed intensity. The deconvolution algorithm is further simplified with an approximate likelihood model (AM-DCV) that can reduce the computational complexity for each iteration. We employ a direct deconvolution method based on the Fourier transform to enhance the initial solution, thereby reducing the number of iterations required for convergence. The M-DCV and AM-DCV algorithms are validated using synthetic and experimental data, demonstrating a maximum improvement of 73% in angular resolution and a sidelobe suppression of 15 dB. Experimental examples demonstrate that the imaging performance of the deconvolution algorithm based on a linear small-aperture array consisting of 16 array elements is comparable to that obtained through conventional beamforming using a linear large-aperture array consisting of 96 array elements. The proposed algorithm is applicable for Ocean Acoustic Waveguide Remote Sensing (OAWRS) and other sensing applications using linear arrays.<\/jats:p>","DOI":"10.3390\/rs16091506","type":"journal-article","created":{"date-parts":[[2024,4,25]],"date-time":"2024-04-25T05:26:13Z","timestamp":1714022773000},"page":"1506","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Maximum Likelihood Deconvolution of Beamforming Images with Signal-Dependent Speckle Fluctuations"],"prefix":"10.3390","volume":"16","author":[{"given":"Yuchen","family":"Zheng","sequence":"first","affiliation":[{"name":"Ocean College, Zhejiang University, Zhoushan 316021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaobin","family":"Ping","sequence":"additional","affiliation":[{"name":"Ocean College, Zhejiang University, Zhoushan 316021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lingxuan","family":"Li","sequence":"additional","affiliation":[{"name":"Ocean College, Zhejiang University, Zhoushan 316021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Delin","family":"Wang","sequence":"additional","affiliation":[{"name":"Ocean College, Zhejiang University, Zhoushan 316021, China"},{"name":"Key Laboratory of Ocean Observation-Imaging Testbed of Zhejiang Province, Zhoushan 316000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,24]]},"reference":[{"key":"ref_1","unstructured":"Urick, R.J. (1983). Principles of Underwater Sound, McGraw Hill."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Van Trees, H.L. (2001). Detection, Estimation, and Modulation Theory, Part I, Wiley-Interscience.","DOI":"10.1002\/0471221090"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Van Trees, H.L. (2002). Optimum Array Processing, John Wiley & Sons.","DOI":"10.1002\/0471221104"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1734","DOI":"10.1126\/science.1169441","article-title":"Critical Population Density Triggers Rapid Formation of Vast Oceanic Fish Shoals","volume":"323","author":"Makris","year":"2009","journal-title":"Science"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1126\/science.1121756","article-title":"Fish population and behavior revealed by instantaneous continental shelf-scale imaging","volume":"311","author":"Makris","year":"2006","journal-title":"Science"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1038\/nature16960","article-title":"Vast assembly of vocal marine mammals from diverse species on fish spawning ground","volume":"531","author":"Wang","year":"2016","journal-title":"Nature"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Huang, W., Wang, D., and Ratilal, P. (2016). Diel and Spatial Dependence of Humpback Song and Non-Song Vocalizations in Fish Spawning Ground. Remote Sens., 8.","DOI":"10.3390\/rs8090712"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"983","DOI":"10.1121\/1.408200","article-title":"Imaging ocean-basin reverberation via inversion","volume":"94","author":"Makris","year":"1993","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2053","DOI":"10.1121\/1.1308047","article-title":"A comparison of bistatic scattering from two geologically distinct abyssal hills","volume":"108","author":"Swee","year":"2000","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1977","DOI":"10.1121\/1.1799252","article-title":"Long range acoustic imaging of the continental shelf environment: The Acoustic Clutter Reconnaissance Experiment 2001","volume":"117","author":"Ratilal","year":"2005","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1408","DOI":"10.1109\/PROC.1969.7278","article-title":"High-Resolution Frequency-Wavenumber Spectrum Analysis","volume":"57","author":"Capon","year":"1969","journal-title":"Proc. IEEE"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1109\/TAP.1986.1143830","article-title":"Multiple Emitter Location and Signal Parameter Estimation","volume":"34","author":"Schmidt","year":"1986","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"4296","DOI":"10.1109\/TSP.2013.2263502","article-title":"\u2113p-MUSIC: Robust Direction-of-Arrival Estimator for Impulsive Noise Environments","volume":"61","author":"Zeng","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1049\/el.2012.4032","article-title":"Low complexity method for DOA estimation using array covariance matrix sparse representation","volume":"49","author":"He","year":"2013","journal-title":"Electron. Lett."},{"key":"ref_15","unstructured":"Abraham, D., and Owsley, N. (1990, January 24\u201326). Beamforming with Dominant Mode Rejection. Proceedings of the IEEE OCEANS \u203290. Engineering in the Ocean Environment, Washington, DC, USA."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1109\/LSP.2013.2266337","article-title":"Robust and Fast Localization of Single Speech Source Using a Planar Array","volume":"20","author":"Ying","year":"2013","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3010","DOI":"10.1109\/TSP.2005.850882","article-title":"Sparse signal reconstruction perspective for source localization with sensor arrays","volume":"53","author":"Malioutov","year":"2005","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"4655","DOI":"10.1109\/TIT.2007.909108","article-title":"Signal Recovery from Random Measurements via Orthogonal Matching Pursuit","volume":"53","author":"Tropp","year":"2008","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2572","DOI":"10.1109\/TSP.2015.2413384","article-title":"Signal Recovery from Random Measurements via Extended Orthogonal Matching Pursuit","volume":"63","author":"Sahoo","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"5702","DOI":"10.1109\/TIT.2014.2338314","article-title":"An Improved RIP-Based Performance Guarantee for Sparse Signal Recovery via Orthogonal Matching Pursuit","volume":"60","author":"Chang","year":"2014","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Yang, Z., and Xie, L. (July, January 29). Continuous Compressed Sensing with a Single or Multiple Measurement Vectors. Proceedings of the 2014 IEEE Workshop on Statistical Signal Processing (SSP), Gold Coast, QLD, Australia.","DOI":"10.1109\/SSP.2014.6884632"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Yang, Z., and Xie, L. (2016, January 20\u201325). On gridless sparse methods for multi-snapshot DOA estimation. Proceedings of the 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Shanghai, China.","DOI":"10.1109\/ICASSP.2016.7472275"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"995","DOI":"10.1109\/TSP.2015.2493987","article-title":"Enhancing Sparsity and Resolution via Reweighted Atomic Norm Minimization","volume":"64","author":"Yang","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1708","DOI":"10.1109\/TSP.2009.2038424","article-title":"Sparse Channel Estimation for Multicarrier Underwater Acoustic Communication: From Subspace Methods to Compressed Sensing","volume":"58","author":"Berger","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_25","unstructured":"Zhang, Y., Sun, H., Xu, F., and Wang, D. (2008, January 20\u201323). OFDM Transform-domain Channel Estimation Based on MMSE for Underwater Acoustic Channels. Proceedings of the 2008 2nd International Conference on Anti-Counterfeiting, Security and Identification, Guiyang, China."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1186\/s13638-021-01995-3","article-title":"M-ary nonlinear sine chirp spread spectrum for underwater acoustic communication based on virtual time-reversal mirror method","volume":"2021","author":"Liu","year":"2021","journal-title":"EURASIP J. Wirel. Commun. Netw."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1109\/MCOM.2010.5621984","article-title":"Application of compressive sensing to sparse channel estimation","volume":"48","author":"Berger","year":"2010","journal-title":"IEEE Commun. Mag."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Liu, Z., Zhou, Q., Gan, W., Qiao, G., and Bilal, M. (2019, January 11\u201313). Adaptive Joint Channel Estimation of Digital Self-Interference Cancelation in Co-time Co-frequency Full-Duplex Underwater Acoustic Communication. Proceedings of the 2019 IEEE International Conference on Signal, Information and Data Processing (ICSIDP), Chongqing, China.","DOI":"10.1109\/ICSIDP47821.2019.9173156"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Zuberi, H., Liu, S., Bilal, M., Alharbi, A., Jaffar, A., Mohsan, S.A.H., Miyajan, A., and Khan, M. (2023). Deep-Neural-Network-Based Receiver Design for Downlink Non-Orthogonal Multiple-Access Underwater Acoustic Communication. J. Mar. Sci. Eng., 11.","DOI":"10.3390\/jmse11112184"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"108742","DOI":"10.1016\/j.apacoust.2022.108742","article-title":"Deep learning-based M-ary spread spectrum communication system in shallow water acoustic channel","volume":"192","author":"Qiao","year":"2022","journal-title":"Appl. Acoust."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"108515","DOI":"10.1016\/j.apacoust.2021.108515","article-title":"Deep learning aided OFDM receiver for underwater acoustic communications","volume":"187","author":"Zhang","year":"2022","journal-title":"Appl. Acoust."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1109\/JOE.2017.2680818","article-title":"Deconvolved Conventional Beamforming for a Horizontal Line Array","volume":"43","author":"Yang","year":"2017","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1121\/10.0001764","article-title":"Deconvolution of decomposed conventional beamforming","volume":"148","author":"Yang","year":"2020","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"18143","DOI":"10.1364\/OE.26.018143","article-title":"Non-linear adaptive three-dimensional imaging with interferenceless coded aperture correlation holography (I-COACH)","volume":"26","author":"Ratnam","year":"2018","journal-title":"Opt. Express"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"210006","DOI":"10.29026\/oes.2022.210006","article-title":"Single-shot mid-infrared incoherent holography using Lucy-Richardson-Rosen algorithm","volume":"1","author":"Anand","year":"2022","journal-title":"Opto-Electron. Sci."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Gopinath, S., Praveen, P.A., Kahro, T., Bleahu, A.-I., Arockiaraj, F., Smith, D., Ng, S.H., Tamm, A., Kukli, K., and Juodkazis, S. (2022). Implementation of a Large-Area Diffractive Lens Using Multiple Sub-Aperture Diffractive Lenses and Computational Reconstruction. Photonics, 10.","DOI":"10.20944\/preprints202211.0281.v1"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Jain, A., and Makris, N. (2016). Maximum Likelihood Deconvolution of Beamformed Images with Signal-Dependent Speckle Fluctuations from Gaussian Random Fields: With Application to Ocean Acoustic Waveguide Remote Sensing (OAWRS). Remote Sens., 8.","DOI":"10.3390\/rs8090694"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1121\/1.416239","article-title":"The effect of saturated transmission scintillation on ocean acoustic intensity measurements","volume":"100","author":"Makris","year":"1996","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2851","DOI":"10.1121\/1.414879","article-title":"Parameter resolution bounds that depend on sample size","volume":"99","author":"Makris","year":"1996","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1121\/1.4726073","article-title":"Scattering from extended targets in range-dependent fluctuating ocean-waveguides with clutter from theory and experiments","volume":"132","author":"Jagannathan","year":"2012","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"3346","DOI":"10.1121\/1.4805668","article-title":"Probability distribution for energy of saturated broadband ocean acoustic transmission: Results from Gulf of Maine 2006 experiment","volume":"133","author":"Tran","year":"2013","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_42","unstructured":"Goodman, J.W. (1985). Statistical Optics, Wiley-Interscience."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Kelley, C. (1999). Iterative Methods for Optimization, Society for Industrial & Applied Mathematics (SIAM).","DOI":"10.1137\/1.9781611970920"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Wang, D., and Ratilal, P. (2017). Angular Resolution Enhancement Provided by Nonuniformly-Spaced Linear Hydrophone Arrays in Ocean Acoustic Waveguide Remote Sensing. Remote Sens., 9.","DOI":"10.3390\/rs9101036"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"2012","DOI":"10.1364\/OL.20.002012","article-title":"A foundation for logarithmic measures of fluctuating intensity in pattern recognition","volume":"20","author":"Makris","year":"1995","journal-title":"Opt. Lett."},{"key":"ref_46","first-page":"147","article-title":"Bounds for tail probabilities of weighted sums of independent gamma random variables","volume":"16","author":"Diaconis","year":"1990","journal-title":"Lect. Notes-Monogr. Ser."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1007\/BF02481056","article-title":"Storage capacity of a dam with gamma type inputs","volume":"34","author":"Mathai","year":"1982","journal-title":"Ann. Inst. Stat. Math."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"541","DOI":"10.1007\/BF02481123","article-title":"The Distribution of the Sum of Independent Gamma Random Variables","volume":"37","author":"Moschopoulos","year":"1985","journal-title":"Ann. Inst. Stat. Math."},{"key":"ref_49","first-page":"205","article-title":"On the convolution of gamma distributions","volume":"31","author":"Akkouchi","year":"2005","journal-title":"Soochow J. Math."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/s40096-015-0169-2","article-title":"Approximations to the distribution of sum of independent non-identically gamma random variables","volume":"9","author":"Murakami","year":"2015","journal-title":"Math. Sci."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1080\/03610918.2014.963612","article-title":"An approximation to the convolution of Gamma Distributions","volume":"46","author":"Barnabani","year":"2015","journal-title":"Commun. Stat. Simul. Comput."},{"key":"ref_52","first-page":"365","article-title":"A Linear Near-Field Interference Cancellation Method Based on Deconvolved Conventional Beamformer Using Fresnel Approximation","volume":"48","author":"Liang","year":"2023","journal-title":"IEEE J. Ocean. Eng. A J. Devoted Appl. Electr. Electron. Eng. Ocean. Environ."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/9\/1506\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:33:33Z","timestamp":1760106813000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/16\/9\/1506"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,24]]},"references-count":52,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2024,5]]}},"alternative-id":["rs16091506"],"URL":"https:\/\/doi.org\/10.3390\/rs16091506","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2024,4,24]]}}}