{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,24]],"date-time":"2025-10-24T08:34:12Z","timestamp":1761294852837,"version":"3.41.0"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2025,6,10]],"date-time":"2025-06-10T00:00:00Z","timestamp":1749513600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,6,10]],"date-time":"2025-06-10T00:00:00Z","timestamp":1749513600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Uppsala Medtech Science and Innovation Centre"},{"DOI":"10.13039\/100007065","name":"Nvidia","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100007065","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100007051","name":"Uppsala University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100007051","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J CARS"],"abstract":"<jats:title>Abstract<\/jats:title>\n          <jats:sec>\n            <jats:title>Purpose<\/jats:title>\n            <jats:p>Speed-of-sound (SoS) is a biomechanical characteristic of tissue, and its imaging can provide a promising biomarker for diagnosis. Reconstructing SoS images from ultrasound acquisitions can be cast as a limited-angle computed-tomography problem, with variational networks being a promising model-based deep learning solution. Some acquired data frames may, however, get corrupted by noise due to, e.g., motion, lack of contact, and acoustic shadows, which in turn negatively affects the resulting SoS reconstructions.\n<\/jats:p>\n          <\/jats:sec>\n          <jats:sec>\n            <jats:title>Methods<\/jats:title>\n            <jats:p>We propose to use the uncertainty in SoS reconstructions to attribute trust to each individual acquired frame. Given multiple acquisitions, we then use an uncertainty-based automatic selection among these retrospectively, to improve diagnostic decisions. We investigate uncertainty estimation based on Monte Carlo Dropout and Bayesian Variational Inference.<\/jats:p>\n          <\/jats:sec>\n          <jats:sec>\n            <jats:title>Results<\/jats:title>\n            <jats:p>We assess our automatic frame selection method for differential diagnosis of breast cancer, distinguishing between benign fibroadenoma and malignant carcinoma. We evaluate 21 lesions classified as BI-RADS\u00a04, which represents suspicious cases for probable malignancy. The most trustworthy frame among four acquisitions of each lesion was identified using uncertainty-based criteria. Selecting a frame informed by uncertainty achieved an area under curve of 76% and 80% for Monte Carlo Dropout and Bayesian Variational Inference, respectively, superior to any uncertainty-uninformed baselines with the best one achieving 64%.<\/jats:p>\n          <\/jats:sec>\n          <jats:sec>\n            <jats:title>Conclusion<\/jats:title>\n            <jats:p>A novel use of uncertainty estimation is proposed for selecting one of multiple data acquisitions for further processing and decision making.<\/jats:p>\n          <\/jats:sec>","DOI":"10.1007\/s11548-025-03402-4","type":"journal-article","created":{"date-parts":[[2025,6,10]],"date-time":"2025-06-10T16:53:00Z","timestamp":1749574380000},"page":"1541-1549","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Uncertainty estimation for trust attribution to speed-of-sound reconstruction with variational networks"],"prefix":"10.1007","volume":"20","author":[{"given":"Sonia","family":"Laguna","sequence":"first","affiliation":[]},{"given":"Lin","family":"Zhang","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1737-0756","authenticated-orcid":false,"given":"Can Deniz","family":"Bezek","sequence":"additional","affiliation":[]},{"given":"Monika","family":"Farkas","sequence":"additional","affiliation":[]},{"given":"Dieter","family":"Schweizer","sequence":"additional","affiliation":[]},{"given":"Rahel A.","family":"Kubik-Huch","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8639-7373","authenticated-orcid":false,"given":"Orcun","family":"Goksel","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,6,10]]},"reference":[{"issue":"5","key":"3402_CR1","doi-asserted-by":"publisher","first-page":"822","DOI":"10.1158\/1055-9965.EPI-20-1193","volume":"30","author":"SC Houghton","year":"2021","unstructured":"Houghton SC, Hankinson SE (2021) Cancer progress and priorities: breast cancer. Cancer Epidemiol Biomark Prev 30(5):822\u2013844","journal-title":"Cancer Epidemiol Biomark Prev"},{"issue":"5","key":"3402_CR2","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1634\/theoncologist.11-5-435","volume":"11","author":"M Guray","year":"2006","unstructured":"Guray M, Sahin AA (2006) Benign breast diseases: classification, diagnosis, and management. Oncologist 11(5):435\u2013449","journal-title":"Oncologist"},{"issue":"2","key":"3402_CR3","doi-asserted-by":"publisher","first-page":"369","DOI":"10.1148\/radiol.13130724","volume":"270","author":"MS Bae","year":"2014","unstructured":"Bae MS, Moon WK, Chang JM, Koo HR, Kim WH, Cho N, Yi A, La Yun B, Lee SH, Kim MY (2014) Breast cancer detected with screening US: reasons for nondetection at mammography. Radiology 270(2):369\u2013377","journal-title":"Radiology"},{"key":"3402_CR4","doi-asserted-by":"publisher","first-page":"3099","DOI":"10.1121\/1.423889","volume":"104","author":"ME Anderson","year":"1998","unstructured":"Anderson ME, Trahey GE (1998) The direct estimation of sound speed using pulse-echo ultrasound. J Acoust Soc Am 104:3099\u2013106","journal-title":"J Acoust Soc Am"},{"key":"3402_CR5","doi-asserted-by":"publisher","first-page":"106309","DOI":"10.1016\/j.ultras.2020.106309","volume":"111","author":"V Perrot","year":"2021","unstructured":"Perrot V, Polichetti M, Varray F, Garcia D (2021) So you think you can DAS? A viewpoint on delay-and-sum beamforming. Ultrasonics 111:106309","journal-title":"Ultrasonics"},{"issue":"1","key":"3402_CR6","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1016\/j.ultrasmedbio.2014.05.019","volume":"41","author":"M Jaeger","year":"2015","unstructured":"Jaeger M, Held G, Peeters S, Preisser S, Gr\u00fcnig M, Frenz M (2015) Computed ultrasound tomography in echo mode for imaging speed of sound using pulse-echo sonography: proof of principle. Ultrasound Med Biol 41(1):235\u2013250","journal-title":"Ultrasound Med Biol"},{"issue":"21","key":"3402_CR7","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6560\/aae2fb","volume":"63","author":"SJ Sanabria","year":"2018","unstructured":"Sanabria SJ, Ozkan E, Rominger M, Goksel O (2018) Spatial domain reconstruction for imaging speed-of-sound with pulse-echo ultrasound: simulation and in vivo study. Phys Med Biol 63(21):215015","journal-title":"Phys Med Biol"},{"issue":"7","key":"3402_CR8","doi-asserted-by":"publisher","first-page":"1201","DOI":"10.1007\/s11548-021-02426-w","volume":"16","author":"R Rau","year":"2021","unstructured":"Rau R, Schweizer D, Vishnevskiy V, Goksel O (2021) Speed-of-sound imaging using diverging waves. Int J Comput Assist Radiol Surg 16(7):1201\u20131211","journal-title":"Int J Comput Assist Radiol Surg"},{"issue":"10","key":"3402_CR9","doi-asserted-by":"publisher","first-page":"1308","DOI":"10.1109\/TUFFC.2023.3303172","volume":"70","author":"D Schweizer","year":"2023","unstructured":"Schweizer D, Rau R, Bezek CD, Kubik-Huch RA, Goksel O (2023) Robust imaging of speed-of-sound using virtual source transmission. IEEE Trans UFFC 70(10):1308\u20131318","journal-title":"IEEE Trans UFFC"},{"key":"3402_CR10","doi-asserted-by":"crossref","unstructured":"Bezek CD, Goksel O (2024) Model-based speed-of-sound reconstruction via interpretable pruned priors. In: IEEE UFFC joint symposium","DOI":"10.1109\/UFFC-JS60046.2024.10794135"},{"key":"3402_CR11","doi-asserted-by":"publisher","first-page":"1490","DOI":"10.1007\/s00330-024-11335-w","volume":"35","author":"CD Bezek","year":"2025","unstructured":"Bezek CD, Farkas M, Schweizer D, Kubik-Huch RA, Goksel O (2025) Breast density assessment via quantitative sound-speed measurement using conventional ultrasound transducers. Eur Radiol 35:1490\u20131501","journal-title":"Eur Radiol"},{"key":"3402_CR12","doi-asserted-by":"publisher","first-page":"1142","DOI":"10.1109\/TBME.2019.2931195","volume":"67","author":"M Feigin","year":"2019","unstructured":"Feigin M, Freedman D, Anthony B (2019) A deep learning framework for single-sided sound speed inversion in medical ultrasound. IEEE Trans Biomed Eng 67:1142\u20131151","journal-title":"IEEE Trans Biomed Eng"},{"issue":"7","key":"3402_CR13","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1097\/RLI.0000000000000553","volume":"54","author":"L Ruby","year":"2019","unstructured":"Ruby L, Sanabria SJ, Martini K, Dedes KJ, Vorburger D, Oezkan E, Frauenfelder T, Goksel O, Rominger MB (2019) Breast cancer assessment with pulse-echo speed of sound ultrasound from intrinsic tissue reflections: proof-of-concept. Invest Radiol 54(7):419\u2013427","journal-title":"Invest Radiol"},{"issue":"7697","key":"3402_CR14","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1038\/nature25988","volume":"555","author":"B Zhu","year":"2018","unstructured":"Zhu B, Liu JZ, Cauley SF, Rosen BR, Rosen MS (2018) Image reconstruction by domain-transform manifold learning. Nature 555(7697):487\u2013492","journal-title":"Nature"},{"issue":"9","key":"3402_CR15","doi-asserted-by":"publisher","first-page":"4509","DOI":"10.1109\/TIP.2017.2713099","volume":"26","author":"KH Jin","year":"2017","unstructured":"Jin KH, McCann M, Froustey E, Unser M (2017) Deep convolutional neural network for inverse problems in imaging. IEEE Trans Image Process 26(9):4509\u20134522","journal-title":"IEEE Trans Image Process"},{"issue":"3","key":"3402_CR16","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1561\/2000000101","volume":"13","author":"MT McCann","year":"2019","unstructured":"McCann MT, Unser M (2019) Biomedical image reconstruction: from the foundations to deep neural networks. Found Trends Signal Process 13(3):283\u2013359","journal-title":"Found Trends Signal Process"},{"issue":"2","key":"3402_CR17","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1109\/MSP.2020.3016905","volume":"38","author":"V Monga","year":"2021","unstructured":"Monga V, Li Y, Eldar YC (2021) Algorithm unrolling: interpretable, efficient deep learning for signal and image processing. IEEE Signal Process Mag 38(2):18\u201344","journal-title":"IEEE Signal Process Mag"},{"issue":"6","key":"3402_CR18","doi-asserted-by":"publisher","first-page":"3055","DOI":"10.1002\/mrm.26977","volume":"79","author":"K Hammernik","year":"2018","unstructured":"Hammernik K, Klatzer T, Kobler E, Recht MP, Sodickson DK, Pock T, Knoll F (2018) Learning a variational network for reconstruction of accelerated MRI data. Magn Reson Med 79(6):3055\u20133071","journal-title":"Magn Reson Med"},{"key":"3402_CR19","doi-asserted-by":"crossref","unstructured":"Vishnevskiy V, Rau R, Goksel O (2019) Deep variational networks with exponential weighting for learning computed tomography. In: Medical image computing and computer assisted intervention (MICCAI), Shenzhen, China, pp 310\u2013318","DOI":"10.1007\/978-3-030-32226-7_35"},{"issue":"12","key":"3402_CR20","doi-asserted-by":"publisher","first-page":"2584","DOI":"10.1109\/TUFFC.2020.3010186","volume":"67","author":"M Bernhardt","year":"2020","unstructured":"Bernhardt M, Vishnevskiy V, Rau R, Goksel O (2020) Training variational networks with multidomain simulations: speed-of-sound image reconstruction. IEEE Trans UFFC 67(12):2584\u20132594","journal-title":"IEEE Trans UFFC"},{"key":"3402_CR21","doi-asserted-by":"crossref","unstructured":"Schlemper J, Castro DC, Bai W, Qin C, Oktay O, Duan J, Price AN, Hajnal J, Rueckert, D (2018) Bayesian deep learning for accelerated MR image reconstruction. In: International workshop on machine learning for medical image reconstruction, pp 64\u201371","DOI":"10.1007\/978-3-030-00129-2_8"},{"issue":"2","key":"3402_CR22","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1109\/TMI.2021.3112040","volume":"41","author":"D Narnhofer","year":"2021","unstructured":"Narnhofer D, Effland A, Kobler E, Hammernik K, Knoll F, Pock T (2021) Bayesian uncertainty estimation of learned variational MRI reconstruction. IEEE Trans Med Imaging 41(2):279\u2013291","journal-title":"IEEE Trans Med Imaging"},{"key":"3402_CR23","doi-asserted-by":"crossref","unstructured":"Ekmekci C, Cetin M (2022) Uncertainty quantification for deep unrolling-based computational imaging. arXiv:2207.00698","DOI":"10.1109\/TCI.2022.3233185"},{"key":"3402_CR24","unstructured":"Gal Y, Ghahramani Z (2016) Dropout as a bayesian approximation: representing model uncertainty in deep learning. In: International conference on machine learning (ICML), pp 1050\u20131059"},{"issue":"1","key":"3402_CR25","doi-asserted-by":"publisher","first-page":"76","DOI":"10.1093\/imamat\/6.1.76","volume":"6","author":"CG Broyden","year":"1970","unstructured":"Broyden CG (1970) The convergence of a class of double-rank minimization algorithms: 1.\u00a0General considerations. IMA J Appl Math 6(1):76\u201390","journal-title":"IMA J Appl Math"},{"key":"3402_CR26","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1007\/s11263-008-0197-6","volume":"82","author":"S Roth","year":"2009","unstructured":"Roth S, Black MJ (2009) Fields of experts. Int J Comput Vis (IJCV) 82:205\u2013229","journal-title":"Int J Comput Vis (IJCV)"},{"key":"3402_CR27","doi-asserted-by":"crossref","unstructured":"Kobler E, Klatzer T, Hammernik K, Pock T (2017) Variational networks: connecting variational methods and deep learning. In: German conference pattern recognition (GCPR), pp 281\u2013293","DOI":"10.1007\/978-3-319-66709-6_23"},{"key":"3402_CR28","doi-asserted-by":"crossref","unstructured":"Bezek CD, Haas M, Rau R, Goksel O (2024) Learning the imaging model of speed-of-sound reconstruction via a convolutional formulation. IEEE Trans Med Imaging (in print). https:\/\/ieeexplore.ieee.org\/document\/10716684","DOI":"10.1109\/TMI.2024.3480690"},{"key":"3402_CR29","doi-asserted-by":"publisher","DOI":"10.1016\/j.ultras.2023.107069","volume":"134","author":"CD Bezek","year":"2023","unstructured":"Bezek CD, Goksel O (2023) Analytical estimation of beamforming speed-of-sound using transmission geometry. Ultrasonics 134:107069","journal-title":"Ultrasonics"}],"container-title":["International Journal of Computer Assisted Radiology and Surgery"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11548-025-03402-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11548-025-03402-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11548-025-03402-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,3]],"date-time":"2025-07-03T14:42:08Z","timestamp":1751553728000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11548-025-03402-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,10]]},"references-count":29,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2025,7]]}},"alternative-id":["3402"],"URL":"https:\/\/doi.org\/10.1007\/s11548-025-03402-4","relation":{},"ISSN":["1861-6429"],"issn-type":[{"type":"electronic","value":"1861-6429"}],"subject":[],"published":{"date-parts":[[2025,6,10]]},"assertion":[{"value":"25 February 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 April 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 June 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Clinical data was collected at Kantonsspital Baden, Switzerland, with informed consent and ethics approval (EKNZ, BASEC 2020-01962).","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics approval and Informed Consent"}}]}}