{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T02:10:44Z","timestamp":1774923044353,"version":"3.50.1"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"6","license":[{"start":{"date-parts":[[2023,10,3]],"date-time":"2023-10-03T00:00:00Z","timestamp":1696291200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2023,10,3]],"date-time":"2023-10-03T00:00:00Z","timestamp":1696291200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100007514","name":"Universit\u00e0 di Pisa","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100007514","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Digit Imaging"],"published-print":{"date-parts":[[2023,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Deep neural networks (DNNs) have already impacted the field of medicine in data analysis, classification, and image processing. Unfortunately, their performance is drastically reduced when datasets are scarce in nature (e.g., rare diseases or early-research data). In such scenarios, DNNs display poor capacity for generalization and often lead to highly biased estimates and silent failures. Moreover, deterministic systems cannot provide epistemic uncertainty, a key component to asserting the model\u2019s reliability. In this work, we developed a probabilistic system for classification as a framework for addressing the aforementioned criticalities. Specifically, we implemented a Bayesian convolutional neural network (BCNN) for the classification of cardiac amyloidosis (CA) subtypes. We prepared four different CNNs: base-deterministic, dropout-deterministic, dropout-Bayesian, and Bayesian. We then trained them on a dataset of 1107 PET images from 47 CA and control patients (data scarcity scenario). The Bayesian model achieved performances (78.28 (1.99) % test accuracy) comparable to the base-deterministic, dropout-deterministic, and dropout-Bayesian ones, while showing strongly increased \u201cOut of Distribution\u201d input detection (validation-test accuracy mismatch reduction). Additionally, both the dropout-Bayesian and the Bayesian models enriched the classification through confidence estimates, while reducing the criticalities of the dropout-deterministic and base-deterministic approaches. This in turn increased the model\u2019s reliability, also providing much needed insights into the network\u2019s estimates. The obtained results suggest that a Bayesian CNN can be a promising solution for addressing the challenges posed by data scarcity in medical imaging classification tasks.<\/jats:p>","DOI":"10.1007\/s10278-023-00897-8","type":"journal-article","created":{"date-parts":[[2023,10,3]],"date-time":"2023-10-03T14:02:17Z","timestamp":1696341737000},"page":"2567-2577","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Bayesian Convolutional Neural Networks in Medical Imaging Classification: A Promising Solution for Deep Learning Limits in Data Scarcity Scenarios"],"prefix":"10.1007","volume":"36","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-6403-0585","authenticated-orcid":false,"given":"Filippo","family":"Bargagna","sequence":"first","affiliation":[]},{"given":"Lisa Anita","family":"De Santi","sequence":"additional","affiliation":[]},{"given":"Nicola","family":"Martini","sequence":"additional","affiliation":[]},{"given":"Dario","family":"Genovesi","sequence":"additional","affiliation":[]},{"given":"Brunella","family":"Favilli","sequence":"additional","affiliation":[]},{"given":"Giuseppe","family":"Vergaro","sequence":"additional","affiliation":[]},{"given":"Michele","family":"Emdin","sequence":"additional","affiliation":[]},{"given":"Assuero","family":"Giorgetti","sequence":"additional","affiliation":[]},{"given":"Vincenzo","family":"Positano","sequence":"additional","affiliation":[]},{"given":"Maria Filomena","family":"Santarelli","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,10,3]]},"reference":[{"key":"897_CR1","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1016\/j.inffus.2020.09.006","volume":"66","author":"F Piccialli","year":"2021","unstructured":"F.\u00a0Piccialli, V.\u00a0Di\u00a0Somma, F.\u00a0Giampaolo, S.\u00a0Cuomo, G.\u00a0Fortino, \u201cA survey on deep learning in medicine: Why, how and when?,\u201d Information Fusion, Elsevier, 66:111\u2013137 (2021).","journal-title":"Information Fusion, Elsevier"},{"key":"897_CR2","doi-asserted-by":"publisher","unstructured":"C.\u00a0Szegedy, W.\u00a0Zaremba, I.\u00a0Sutskever, J.\u00a0Bruna, D.\u00a0Erhan, I.\u00a0Goodfellow, R.\u00a0Fergus, \u201cIntriguing properties of neural networks,\u201d arXiv preprint, https:\/\/doi.org\/10.48550\/arXiv:1312.6199 (December 21, 2013).","DOI":"10.48550\/arXiv:1312.6199"},{"key":"897_CR3","doi-asserted-by":"publisher","first-page":"9375","DOI":"10.1109\/ACCESS.2017.2788044","volume":"6","author":"J Ker","year":"2017","unstructured":"J.\u00a0Ker, L.\u00a0Wang, J.\u00a0Rao, T.\u00a0Lim, \u201cDeep learning applications in medical image analysis,\u201d IEEE Access, 6:9375\u20139389 (2017).","journal-title":"IEEE Access"},{"issue":"1","key":"897_CR4","first-page":"1929","volume":"15","author":"N Srivastava","year":"2014","unstructured":"N.\u00a0Srivastava, G.\u00a0Hinton, A.\u00a0Krizhevsky, I.\u00a0Sutskever, R.\u00a0Salakhutdinov, \u201cDropout: a simple way to prevent neural networks from overfitting,\u201d The journal of machine learning research, 15:1:1929\u20131958 (2014).","journal-title":"The journal of machine learning research"},{"issue":"1","key":"897_CR5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s40537-018-0162-3","volume":"6","author":"C Shorten","year":"2019","unstructured":"C.\u00a0Shorten, T.\u00a0M. Khoshgoftaar, \u201cA survey on image data augmentation for deep learning,\u201d Journal of big data, Springer, 6:1:1\u201348 (2019).","journal-title":"Journal of big data, Springer"},{"key":"897_CR6","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1007\/s11222-009-9153-8","volume":"21","author":"T Fushiki","year":"2011","unstructured":"T.\u00a0Fushiki, \u201cEstimation of prediction error by using k-fold cross-validation,\u201d Statistics and Computing, Springer, 21:137\u2013146 (2011).","journal-title":"Statistics and Computing, Springer"},{"key":"897_CR7","unstructured":"S.\u00a0Depeweg, J.-M. Hernandez-Lobato, F.\u00a0Doshi-Velez, S.\u00a0Udluft, \u201cDecomposition of uncertainty in bayesian deep learning for efficient and risk-sensitive learning,\u201d in International Conference on Machine Learning, 1184\u20131193 (2018)."},{"issue":"2","key":"897_CR8","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1109\/MCI.2022.3155327","volume":"17","author":"LV Jospin","year":"2022","unstructured":"L.\u00a0V. Jospin, H.\u00a0Laga, F.\u00a0Boussaid, W.\u00a0Buntine, M.\u00a0Bennamoun, \u201cHands-on bayesian neural networks\u2013a tutorial for deep learning users,\u201d IEEE Computational Intelligence Magazine, 17:2:29\u201348 (2022).","journal-title":"IEEE Computational Intelligence Magazine"},{"key":"897_CR9","doi-asserted-by":"crossref","unstructured":"\u0141.\u00a0Raczkowski, M.\u00a0Mo\u017cejko, J.\u00a0Zambonelli, E.\u00a0Szczurek, \u201cAra: accurate, reliable and active histopathological image classification framework with bayesian deep learning,\u201d Scientific reports, Nature, 9:1:Article number: 14347 (2019).","DOI":"10.1038\/s41598-019-50587-1"},{"issue":"10","key":"897_CR10","doi-asserted-by":"publisher","first-page":"6422","DOI":"10.1364\/BOE.432365","volume":"12","author":"B Song","year":"2021","unstructured":"B.\u00a0Song, S.\u00a0Sunny, S.\u00a0Li, K.\u00a0Gurushanth, P.\u00a0Mendonca, N.\u00a0Mukhia, S.\u00a0Patrick, S.\u00a0Gurudath, S.\u00a0Raghavan, I.\u00a0Tsusennaro, S.\u00a0T. Leivon, T.\u00a0Kolur, V.\u00a0Shetty, V.\u00a0R. Bushan, R.\u00a0Ramesh, T.\u00a0Peterson, V.\u00a0Pillai, P.\u00a0Wilder-Smith, A.\u00a0Sigamani, A.\u00a0Suresh, A.\u00a0Kuriakose, P.\u00a0Birur, R.\u00a0Liang, \u201cBayesian deep learning for reliable oral cancer image classification,\u201d Biomedical Optics Express, Optica Publishing Group, 12:10:6422\u20136430 (2021).","journal-title":"Biomedical Optics Express, Optica Publishing Group"},{"key":"897_CR11","doi-asserted-by":"publisher","unstructured":"S.\u00a0Yadav, \u201cBayesian deep learning based convolutional neural network for classification of parkinson\u2019s disease using functional magnetic resonance images,\u201d SSRN, https:\/\/doi.org\/10.2139\/ssrn.3833760 (April 25, 2021).","DOI":"10.2139\/ssrn.3833760"},{"key":"897_CR12","doi-asserted-by":"publisher","first-page":"36538","DOI":"10.1109\/ACCESS.2022.3163384","volume":"10","author":"AA Abdullah","year":"2022","unstructured":"A.\u00a0A. Abdullah, M.\u00a0H. Masoud, T.\u00a0M. Yaseen, \u201cA review on bayesian deep learning in healthcare: Applications and challenges,\u201d IEEE Access, 10:36538\u201336562 (2022).","journal-title":"IEEE Access"},{"issue":"518","key":"897_CR13","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1080\/01621459.2017.1285773","volume":"112","author":"DM Blei","year":"2017","unstructured":"D.\u00a0M. Blei, A.\u00a0Kucukelbir, J.\u00a0D. McAuliffe, \u201cVariational inference: A review for statisticians,\u201d Journal of the American statistical Association, 112:518:859\u2013877 (2017).","journal-title":"Journal of the American statistical Association"},{"key":"897_CR14","doi-asserted-by":"crossref","unstructured":"C.\u00a0J. Geyer, \u201cIntroduction to markov chain monte carlo,\u201d Handbook of markov chain monte carlo, Chapter 1 20116022, Boca Raton (2011).","DOI":"10.1201\/b10905-2"},{"key":"897_CR15","unstructured":"Y.\u00a0Gal, Z.\u00a0Ghahramani, \u201cDropout as a bayesian approximation: Representing model uncertainty in deep learning,\u201d in International Conference on Machine Learning, 1050\u20131059 (2016)."},{"key":"897_CR16","doi-asserted-by":"publisher","unstructured":"V.\u00a0Mullachery, A.\u00a0Khera, A.\u00a0Husain, \u201cBayesian neural networks,\u201d arXiv preprint, https:\/\/doi.org\/10.48550\/arXiv:1801.07710 (January 23, 2018).","DOI":"10.48550\/arXiv:1801.07710"},{"key":"897_CR17","unstructured":"C.\u00a0Blundell, J.\u00a0Cornebise, K.\u00a0Kavukcuoglu, D.\u00a0Wierstra, \u201cWeight uncertainty in neural network,\u201d in International Conference on Machine Learning, 1613\u20131622 (2015)."},{"key":"897_CR18","unstructured":"D.\u00a0P. Kingma, T.\u00a0Salimans, M.\u00a0Welling, \u201cVariational dropout and the local reparameterization trick,\u201d Advances in neural information processing systems 28, NIPS (2015)."},{"issue":"10038","key":"897_CR19","doi-asserted-by":"publisher","first-page":"2641","DOI":"10.1016\/S0140-6736(15)01274-X","volume":"387","author":"AD Wechalekar","year":"2016","unstructured":"A.\u00a0D. Wechalekar, J.\u00a0D. Gillmore, P.\u00a0N. Hawkins, \u201cSystemic amyloidosis,\u201d The Lancet, Elsevier, 387:10038:2641\u20132654 (2016).","journal-title":"The Lancet, Elsevier"},{"issue":"Suppl. 2","key":"897_CR20","first-page":"30","volume":"18","author":"A Martinez-Naharro","year":"2018","unstructured":"A.\u00a0Martinez-Naharro, P.\u00a0N. Hawkins, M.\u00a0Fontana, \u201cCardiac amyloidosis,\u201d Clinical Medicine, Royal College of Physicians, 18:Suppl.2:30\u201335 (2018).","journal-title":"Clinical Medicine, Royal College of Physicians"},{"key":"897_CR21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1756-8722-4-1","volume":"4","author":"M Rosenzweig","year":"2011","unstructured":"M.\u00a0Rosenzweig, H.\u00a0Landau, \u201cLight chain (al) amyloidosis: update on diagnosis and management,\u201d Journal of Hematology & Oncology, Springer, 4:1\u20138 (2011).","journal-title":"Journal of Hematology & Oncology, Springer"},{"issue":"22","key":"897_CR22","doi-asserted-by":"publisher","first-page":"2872","DOI":"10.1016\/j.jacc.2019.04.003","volume":"73","author":"FL Ruberg","year":"2019","unstructured":"F.\u00a0L. Ruberg, M.\u00a0Grogan, M.\u00a0Hanna, J.\u00a0W. Kelly, M.\u00a0S. Maurer, \u201cTransthyretin amyloid cardiomyopathy: Jacc state-of-the-art review,\u201d Journal of the American College of Cardiology, JACC, 73:22:2872\u20132891 (2019).","journal-title":"Journal of the American College of Cardiology, JACC"},{"issue":"7","key":"897_CR23","doi-asserted-by":"publisher","first-page":"2327","DOI":"10.1007\/s10554-021-02190-7","volume":"37","author":"MF Santarelli","year":"2021","unstructured":"M.\u00a0F. Santarelli, D.\u00a0Genovesi, V.\u00a0Positano, M.\u00a0Scipioni, G.\u00a0Vergaro, B.\u00a0Favilli, A.\u00a0Giorgetti, M.\u00a0Emdin, L.\u00a0Landini, P.\u00a0Marzullo, \u201cDeep-learning-based cardiac amyloidosis classification from early acquired pet images,\u201d The International Journal of Cardiovascular Imaging, Springer, 37:7:2327\u20132335 (2021).","journal-title":"The International Journal of Cardiovascular Imaging, Springer"},{"issue":"16","key":"897_CR24","doi-asserted-by":"publisher","first-page":"1878","DOI":"10.2174\/1381612826666200813133557","volume":"27","author":"M Santarelli","year":"2021","unstructured":"M.\u00a0Santarelli, M.\u00a0Scipioni, D.\u00a0Genovesi, A.\u00a0Giorgetti, P.\u00a0Marzullo, L.\u00a0Landini, \u201cImaging techniques as an aid in the early detection of cardiac amyloidosis.,\u201d Current Pharmaceutical Design, Bentham Science, 27:16:1878\u20131889 (2021).","journal-title":"Current Pharmaceutical Design, Bentham Science"},{"key":"897_CR25","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1007\/s12350-018-1365-x","volume":"27","author":"YJ Kim","year":"2020","unstructured":"Y.\u00a0J. Kim, S.\u00a0Ha, Y.-i. Kim, \u201cCardiac amyloidosis imaging with amyloid positron emission tomography: a systematic review and meta-analysis,\u201d Journal of Nuclear Cardiology, Springer, 27:123\u2013132 (2020).","journal-title":"Journal of Nuclear Cardiology, Springer"},{"issue":"1","key":"897_CR26","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1016\/j.jcmg.2020.05.031","volume":"14","author":"D Genovesi","year":"2021","unstructured":"D.\u00a0Genovesi, G.\u00a0Vergaro, A.\u00a0Giorgetti, P.\u00a0Marzullo, M.\u00a0Scipioni, M.\u00a0F. Santarelli, A.\u00a0Pucci, G.\u00a0Buda, E.\u00a0Volpi, M.\u00a0Emdin, \u201c[18f]-florbetaben pet\/ct for differential diagnosis among cardiac immunoglobulin light chain, transthyretin amyloidosis, and mimicking conditions,\u201d Cardiovascular Imaging, JACC, 14:1:246\u2013255 (2021).","journal-title":"Cardiovascular Imaging, JACC"},{"issue":"2","key":"897_CR27","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1111\/bjh.13156","volume":"168","author":"JD Gillmore","year":"2015","unstructured":"J.\u00a0D. Gillmore, A.\u00a0Wechalekar, J.\u00a0Bird, J.\u00a0Cavenagh, S.\u00a0Hawkins, M.\u00a0Kazmi, H.\u00a0J. Lachmann, P.\u00a0N. Hawkins, G.\u00a0Pratt, B.\u00a0Committee, \u201cGuidelines on the diagnosis and investigation of al amyloidosis,\u201d British journal of haematology, 168:2:207\u2013218 (2015).","journal-title":"British journal of haematology"},{"issue":"24","key":"897_CR28","doi-asserted-by":"publisher","first-page":"2404","DOI":"10.1161\/CIRCULATIONAHA.116.021612","volume":"133","author":"JD Gillmore","year":"2016","unstructured":"J.\u00a0D. Gillmore, M.\u00a0S. Maurer, R.\u00a0H. Falk, G.\u00a0Merlini, T.\u00a0Damy, A.\u00a0Dispenzieri, A.\u00a0D. Wechalekar, J.\u00a0L. Berk, C.\u00a0C. Quarta, M.\u00a0Grogan, H.\u00a0J. Lachmann, S.\u00a0Bokhari, A.\u00a0Castano, S.\u00a0Dorbala, G.\u00a0B. Johnson, A.\u00a0W. J.\u00a0M. Glaudemans, T.\u00a0Rezk, M.\u00a0Fontana, G.\u00a0Palladini, P.\u00a0Milani, P.\u00a0L. Guidalotti, K.\u00a0Flatman, T.\u00a0Lane, F.\u00a0W. Vonberg, C.\u00a0J. Whelan, J.\u00a0C. Moon, F.\u00a0L. Ruberg, E.\u00a0J. Miller, D.\u00a0F. Hutt, B.\u00a0P. Hazenberg, C.\u00a0Rapezzi, P.\u00a0N. Hawkins, \u201cNonbiopsy diagnosis of cardiac transthyretin amyloidosis,\u201d Circulation, AHA, 133:24:2404\u20132412 (2016).","journal-title":"Circulation, AHA"},{"key":"897_CR29","doi-asserted-by":"crossref","unstructured":"S.\u00a0Imambi, K.\u00a0B. Prakash, G.\u00a0Kanagachidambaresan, \u201cPytorch,\u201d Programming with TensorFlow: Solution for Edge Computing Applications, Springer, 87\u2013104 (2021).","DOI":"10.1007\/978-3-030-57077-4_10"},{"key":"897_CR30","unstructured":"P.\u00a0Esposito, \u201cBlitz - bayesian layers in torch zoo (a bayesian deep learing library for torch), github.\u201d https:\/\/github.com\/piEsposito\/blitz-bayesian-deep-learning\/ (2020)."},{"key":"897_CR31","doi-asserted-by":"publisher","unstructured":"T.\u00a0DeVries, W.\u00a0T. Graham, \u201cLearning confidence for out-of-distribution detection in neural networks,\u201d arXiv preprint, https:\/\/doi.org\/10.48550\/arXiv.1802.04865 (February 13, 2018).","DOI":"10.48550\/arXiv.1802.04865"},{"key":"897_CR32","doi-asserted-by":"crossref","unstructured":"A.\u00a0Uchendu, D.\u00a0Campoy, C.\u00a0Menart, A.\u00a0Hildenbrandt, \u201cRobustness of bayesian neural networks to white-box adversarial attacks,\u201d in 2021 IEEE Fourth International Conference on Artificial Intelligence and Knowledge Engineering (AIKE), 72\u201380 (2021).","DOI":"10.1109\/AIKE52691.2021.00017"}],"container-title":["Journal of Digital Imaging"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10278-023-00897-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10278-023-00897-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10278-023-00897-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,12,18]],"date-time":"2023-12-18T21:54:28Z","timestamp":1702936468000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10278-023-00897-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,3]]},"references-count":32,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2023,12]]}},"alternative-id":["897"],"URL":"https:\/\/doi.org\/10.1007\/s10278-023-00897-8","relation":{},"ISSN":["0897-1889","1618-727X"],"issn-type":[{"value":"0897-1889","type":"print"},{"value":"1618-727X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,10,3]]},"assertion":[{"value":"13 April 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 August 2023","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 August 2023","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 October 2023","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"Relating to the data used in this article, both the AIFA (Agenzia Italiana del Farmaco) committee and the institutional ethics committee gave their approval to the study. The research complied with the Helsinki Declaration.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethics Approval"}},{"value":"Nicola Martini is presently an employee of Yunu Inc.; his collaboration to the present study occurred before its present affiliation, his contribution to this article reflects entirely and only his own expertise on the matter, and he declares no competing financial or non-financial interests related to the present article. All the other authors do not have competing financial or non-financial interests to disclose concerning the present manuscript.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of Interest"}}]}}