{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T07:40:09Z","timestamp":1762069209278,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2022,10,6]],"date-time":"2022-10-06T00:00:00Z","timestamp":1665014400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Foundation for Science and Technology Development (NAFOSTED)","award":["103.05-2020.13"],"award-info":[{"award-number":["103.05-2020.13"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electronics"],"abstract":"<jats:p>In ultrasound tomography, cross-sectional images represent the spatial distribution of the physical parameters of a target of interest, which can be obtained based on scattered ultrasound measurements. These measurements can be obtained from dense datasets collected at different transmitter and receiver locations, and using multiple frequencies. The Born approximation method, which provides a simple linear relationship between the objective function and the scattering field, has been adopted to resolve the inverse scattering problem. The distorted Born iterative method (DBIM), which utilizes the first-order Born approximation, is a productive diffraction tomography scheme. In this article, the range of interpolation applications is extended at the multilayer level, taking into account the advantages of integrating this multilayer level with multiple frequencies for the DBIM. Specifically, we consider: (a) a multi-resolution technique, i.e., a multi-step interpolation for the DBIM: MR-DBIM, with the advantage that the normalized absolute error is reduced by 18.67% and 37.21% in comparison with one-step interpolation DBIM and typical DBIM, respectively; (b) the integration of multi-resolution and multi-frequency techniques with the DBIM: MR-MF-DBIM, which is applied to image targets with high sound contrast in a strongly scattering medium. Relative to MR-DBIM, this integration offers a 44.01% reduction in the normalized absolute error.<\/jats:p>","DOI":"10.3390\/electronics11193203","type":"journal-article","created":{"date-parts":[[2022,10,8]],"date-time":"2022-10-08T04:04:56Z","timestamp":1665201896000},"page":"3203","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["High Sound-Contrast Inverse Scattering by MR-MF-DBIM Scheme"],"prefix":"10.3390","volume":"11","author":[{"given":"Luong Thi","family":"Theu","sequence":"first","affiliation":[{"name":"Institute of Applied Technology, Thu Dau Mot University, Binh Duong 820000, Vietnam"}]},{"given":"Tran","family":"Quang-Huy","sequence":"additional","affiliation":[{"name":"Faculty of Physics, Hanoi Pedagogical University 2, Hanoi 100000, Vietnam"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2457-2145","authenticated-orcid":false,"given":"Tran","family":"Duc-Nghia","sequence":"additional","affiliation":[{"name":"Institute of Information Technology, Vietnam Academy of Science and Technology, Hanoi 100000, Vietnam"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5784-1052","authenticated-orcid":false,"given":"Vijender Kumar","family":"Solanki","sequence":"additional","affiliation":[{"name":"CMR Institute of Technology, Hyderabad, Telangana 501401, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7673-388X","authenticated-orcid":false,"given":"Tran","family":"Duc-Tan","sequence":"additional","affiliation":[{"name":"Faculty of Electrical and Electronic Engineering, Phenikaa University, Hanoi 12116, Vietnam"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7603-6526","authenticated-orcid":false,"given":"Jo\u00e3o Manuel R. S.","family":"Tavares","sequence":"additional","affiliation":[{"name":"Instituto de Ci\u00eancia e Inova\u00e7\u00e3o em Engenharia Mec\u00e2nica e Engenharia Industrial, Departamento de Engenharia Mec\u00e2nica, Faculdade de Engenharia, Universidade do Porto, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1109\/T-SU.1984.31501","article-title":"Fundamentals of digital ultrasonic processing","volume":"31","author":"Schueler","year":"1984","journal-title":"IEEE Trans. Sonics Ultrason."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1109\/PROC.1979.11278","article-title":"Ultrasonic imaging using arrays","volume":"67","author":"Macovski","year":"1979","journal-title":"Proc. IEEE"},{"key":"ref_3","unstructured":"Kino, G.S. (1987). Acoustic Waves: Devices, Imaging, and Analog Signal Processing. Englewood Cliffs, Prentice Hall."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1109\/58.248219","article-title":"Wavefront amplitude distortion and image sidelobe levels: Part I\u2014Theory and computer simulations","volume":"40","author":"Zhu","year":"1993","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/978-1-4615-8216-8_4","article-title":"Algebraic reconstruction of spatial distributions of acoustic velocities in tissue from their time-of-flight profiles","volume":"6","author":"Greenleaf","year":"1975","journal-title":"Acoust. Hologr."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"591","DOI":"10.1007\/978-1-4757-0827-1_34","article-title":"Algebraic reconstruction of spatial distributions of acoustic absorption within tissue from their two-dimensional acoustic projections","volume":"5","author":"Greenleaf","year":"1974","journal-title":"Acoust. Hologr."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Johnson, S.A., Greenleaf, J.F., Samayoa, W.A., Duck, F.A., and Sjostrand, J. (1975, January 22\u201324). Reconstruction of three-dimensional velocity fields and other parameters by acoustic ray tracing. Proceedings of the IEEE Ultrasonics Symposium, Los Angeles, CA, USA.","DOI":"10.1109\/ULTSYM.1975.196462"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1375","DOI":"10.1118\/1.1897463","article-title":"Development of ultrasound tomography for breast imaging: Technical assessment","volume":"32","author":"Duric","year":"2005","journal-title":"Med. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Li, C., Duric, N., and Huang, L. (2008, January 27\u201330). Breast imaging using transmission ultrasound: Reconstructing tissue parameters of sound speed and attenuation. Proceedings of the International Conference on BioMedical Engineering and Informatics, Sanya, China.","DOI":"10.1109\/BMEI.2008.303"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1109\/TMI.2004.843179","article-title":"Soft tissue differentiation using multiband signatures of high resolution ultrasonic transmission tomography","volume":"24","author":"Jeong","year":"2005","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1007\/1-4020-5721-0_17","article-title":"Noninvasive breast tissue characterization using ultrasound speed and attenuation","volume":"28","author":"Johnson","year":"2007","journal-title":"Acoust. Imaging"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Kak, A., and Slaney, M. (2001). Principles of Computerized Tomographic Imaging. Philadelphia, SIAM.","DOI":"10.1137\/1.9780898719277"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1109\/MEMB.1987.5006465","article-title":"Ultrasonic computed tomography for breast examination","volume":"6","author":"Greenleaf","year":"1987","journal-title":"IEEE Eng. Med. Biol. Mag."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1002\/(SICI)1098-1098(1997)8:1<137::AID-IMA15>3.0.CO;2-#","article-title":"High-speed data acquisition in a diffraction tomography system employing large-scale toroidal arrays","volume":"8","author":"Andre","year":"1997","journal-title":"Int. J. Imaging Syst. Technol."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/1-4020-5721-0_20","article-title":"Full wave, nonlinear, inverse scattering","volume":"28","author":"Wiskin","year":"2007","journal-title":"Acoust. Imaging"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Lasaygues, P., Franceschini, E., Guillermin, R., Lefebvre, J.-P., Salaud, N., and Petit, P. (2007, January 28\u201331). Two-dimensional ultrasonic computed tomography of growing bones. Proceedings of the IEEE Ultrasonics Symposium, New York, NY, USA.","DOI":"10.1109\/ULTSYM.2007.457"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1364\/OL.7.000111","article-title":"Inversion formula for inverse scattering within the Born approximation","volume":"7","author":"Devaney","year":"1982","journal-title":"Opt. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1364\/OL.6.000374","article-title":"Inverse-scattering theory within the Rytov approximation","volume":"6","author":"Devaney","year":"1981","journal-title":"Opt. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"218","DOI":"10.1109\/42.56334","article-title":"Reconstruction of two-dimensional permittivity distribution using the distorted Born iterative method","volume":"9","author":"Chew","year":"1990","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_20","unstructured":"Haddadin, O.S., and Ebbini, E.S. (1995, January 7\u201310). Solution to the inverse scattering problem using a modified distorted Born iterative algorithm. Proceedings of the IEEE Ultrasonics Symposium, Seattle, WA, USA."},{"key":"ref_21","unstructured":"Gang, Y., Lim, K.H., George, R., Ybarra, G., Joines, W.T., and Liu, Q.H. (2006, January 6\u20139). A 3D EIT system for breast cancer imaging. Proceedings of the 3rd IEEE International Symposium on Biomedical Imaging: Nano to Macro, Arlington, VA, USA."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Abdi, M., and Liatsis, P. (2011, January 6\u20138). EIT in Breast Cancer Imaging: Application to Patient-Specific Forward Model. Proceedings of the 2011 Developments in E-systems Engineering, Dubai, United Arab Emirates.","DOI":"10.1109\/DeSE.2011.98"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1007\/s42600-021-00192-x","article-title":"Interpolated Hybrid DBIM Approach for Enhanced Imaging in Ultrasound Tomography","volume":"38","author":"Nguyen","year":"2022","journal-title":"Res. Biomed. Eng. (RBME)"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1080\/17445760.2021.1967350","article-title":"Influence of the multi-resolution technique on tomographic reconstruction in ultrasound tomography","volume":"36","author":"Theu","year":"2021","journal-title":"Int. J. Parallel Emergent Distrib. Syst."},{"key":"ref_25","first-page":"1","article-title":"An Enhanced Multi-Frequency Distorted Born Iterative Method for Ultrasound Tomography Based on Fundamental Tone and Overtones","volume":"12","author":"Nguyen","year":"2022","journal-title":"Int. J. Inf. Retr. Res. (IJIRR)"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Haddadin, O.S., and Ebbini, E.S. (1997). Multiple frequency distorted Born iterative method for tomographic imaging. Acoustical Imaging, Springer.","DOI":"10.1007\/978-1-4419-8588-0_96"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1485","DOI":"10.1109\/58.738288","article-title":"Imaging strongly scattering media using a multiple frequency distorted Born iterative method","volume":"45","author":"Haddadin","year":"1998","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1635","DOI":"10.1088\/0266-5611\/17\/6\/307","article-title":"Multiple-frequency distorted-wave Born approach to 2D inverse profiling","volume":"17","author":"Tijhuis","year":"2001","journal-title":"Inverse Probl."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2471","DOI":"10.1109\/TUFFC.2010.1713","article-title":"Density imaging using a multiple-frequency DBIM approach","volume":"57","author":"Lavarello","year":"2010","journal-title":"IEEE Trans. Ultrason. Ferroelectr. Freq. Control"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1177\/0037549716630605","article-title":"Influence of dual-frequency combination on the quality improvement of ultrasound tomography","volume":"92","author":"Tran","year":"2016","journal-title":"Simulation"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Varray, F., Cachard, C., Kybic, J., Novell, A., Bouakaz, A., and Basset, O. (2012, January 27\u201331). A multi-frequency approach to increase the native resolution of ultrasound images. Proceedings of the 20th European Signal Processing Conference (EUSIPCO), Bucharest, Romania.","DOI":"10.1109\/ISBI.2012.6235756"},{"key":"ref_32","first-page":"304","article-title":"Multi-frequency ultrasound imaging: Phantom study","volume":"2","author":"Sayed","year":"2018","journal-title":"Int. J. Allied Health Sci."},{"key":"ref_33","unstructured":"Miao, Z. (2018). Implementation and Optimisation of Microwave Medical Imaging Based on the Multiple-Frequency Dbim-Twist Algorithm. [Ph.D. Thesis, King\u2019s College London]."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Ahsan, S., Guo, Z., Miao, Z., Sotiriou, I., Koutsoupidou, M., Kallos, E., and Kosmas, P. (2018). Design and experimental validation of a multiple-frequency microwave tomography system employing the DBIM-TwIST algorithm. Sensors, 18.","DOI":"10.3390\/s18103491"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2507","DOI":"10.1109\/TAP.2017.2679067","article-title":"Multiple-frequency DBIM-TwIST algorithm for microwave breast imaging","volume":"65","author":"Miao","year":"2017","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"5187","DOI":"10.1109\/TAP.2020.3044806","article-title":"Enhanced FEM-based DBIM approach for two-dimensional microwave imaging","volume":"69","author":"Lu","year":"2020","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1109\/TCI.2022.3146815","article-title":"Hybrid Approaches in Microwave Imaging using Quantitative Time-and Frequency-Domain Algorithms","volume":"8","author":"Saraskanroud","year":"2022","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"ref_38","unstructured":"Krainov, V.P., Reiss, R.H., and Smirnov, M.B. (2005). Appendix J: Properties of the Generalized Bessel Function. Radiative Processes in Atomic Physics, John Wiley & Sons."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1137\/S0895479897326432","article-title":"Tikhonov Regularization and Total Least Squares","volume":"21","author":"Golub","year":"1999","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1109\/TPAMI.2010.57","article-title":"Product quantization for nearest neighbor search","volume":"33","author":"Jegou","year":"2011","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1109\/TBME.1981.324789","article-title":"Clinical imaging transmissive ultrasonic computerized tomography","volume":"28","author":"Greenleaf","year":"1981","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1813","DOI":"10.1121\/1.4913774","article-title":"Ultrasound tomography for simultaneous reconstruction of acoustic density, attenuation, and compressibility profiles","volume":"134","author":"Mojabi","year":"2015","journal-title":"J. Acoust. Soc. Am."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"860","DOI":"10.1109\/TMTT.1984.1132783","article-title":"Limitations of imaging with first order diffraction tomography","volume":"32","author":"Slaney","year":"1984","journal-title":"IEEE Trans. Microw. Theory Tech."}],"container-title":["Electronics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-9292\/11\/19\/3203\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:47:10Z","timestamp":1760143630000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-9292\/11\/19\/3203"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,6]]},"references-count":43,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["electronics11193203"],"URL":"https:\/\/doi.org\/10.3390\/electronics11193203","relation":{},"ISSN":["2079-9292"],"issn-type":[{"type":"electronic","value":"2079-9292"}],"subject":[],"published":{"date-parts":[[2022,10,6]]}}}