{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T12:16:54Z","timestamp":1763468214882},"reference-count":18,"publisher":"MIT Press - Journals","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Neural Computation"],"published-print":{"date-parts":[[2015,1]]},"abstract":"<jats:p> Deep learning has traditionally been computationally expensive, and advances in training methods have been the prerequisite for improving its efficiency in order to expand its application to a variety of image classification problems. In this letter, we address the problem of efficient training of convolutional deep belief networks by learning the weights in the frequency domain, which eliminates the time-consuming calculation of convolutions. An essential consideration in the design of the algorithm is to minimize the number of transformations to and from frequency space. We have evaluated the running time improvements using two standard benchmark data sets, showing a speed-up of up to 8\u00a0times on 2D images and up to 200\u00a0times on 3D volumes. Our training algorithm makes training of convolutional deep belief networks on 3D medical images with a resolution of up to 128 \u00d7 128 \u00d7 128 voxels practical, which opens new directions for using deep learning for medical image analysis. <\/jats:p>","DOI":"10.1162\/neco_a_00682","type":"journal-article","created":{"date-parts":[[2014,11,7]],"date-time":"2014-11-07T19:42:44Z","timestamp":1415389364000},"page":"211-227","source":"Crossref","is-referenced-by-count":46,"title":["Efficient Training of Convolutional Deep Belief Networks in the Frequency Domain for Application to High-Resolution 2D and 3D Images"],"prefix":"10.1162","volume":"27","author":[{"given":"Tom","family":"Brosch","sequence":"first","affiliation":[{"name":"MS\/MRI Research Group, Vancouver, BC V6T 2B5, Canada, and Department of Electrical and Computer Engineering, University of British Columbia, Vancouver, BC V6T 1Z4, Canada"}]},{"given":"Roger","family":"Tam","sequence":"additional","affiliation":[{"name":"MS\/MRI Research Group, Vancouver, BC V6T 2B5, Canada, and Department of Radiology, University of British Columbia, Vancouver, BC V5Z 1M9, Canada"}]}],"member":"281","reference":[{"key":"B1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-40763-5_78"},{"key":"B2","first-page":"1","volume-title":"Advances in neural information processing systems, 25","author":"Ciresan D.","year":"2012"},{"key":"B3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-40763-5_50"},{"key":"B4","doi-asserted-by":"publisher","DOI":"10.1109\/CVPR.2009.5206848"},{"key":"B5","doi-asserted-by":"publisher","DOI":"10.1162\/089976602760128018"},{"key":"B6","doi-asserted-by":"publisher","DOI":"10.1162\/neco.2006.18.7.1527"},{"key":"B9","first-page":"1","volume-title":"Advances in neural information processing systems, 25","author":"Krizhevsky A.","year":"2012"},{"key":"B10","doi-asserted-by":"publisher","DOI":"10.1145\/1553374.1553453"},{"key":"B11","doi-asserted-by":"publisher","DOI":"10.1145\/2001269.2001295"},{"key":"B12","doi-asserted-by":"publisher","DOI":"10.1109\/ISBI.2011.5872414"},{"key":"B13","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-40763-5_32"},{"key":"B14","doi-asserted-by":"publisher","DOI":"10.1162\/jocn.2007.19.9.1498"},{"key":"B15","first-page":"1","author":"Mathieu M.","year":"2014","journal-title":"Proceedings of the 2nd International Conference on Learning Representations"},{"key":"B16","first-page":"807","volume-title":"Proceedings of the 27th Annual International Conference on Machine Learning","author":"Nair V.","year":"2010"},{"key":"B17","doi-asserted-by":"publisher","DOI":"10.1145\/1553374.1553486"},{"key":"B18","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-15825-4_10"},{"key":"B19","doi-asserted-by":"crossref","unstructured":"Wu, G., Kim, M., Wang, Q. & Gao, Y. (2013). Unsupervised deep feature learning for deformable registration of MR brain images. In K. Mori, I. Sakuma, Y. Sato, C. Barillot, & N. Navab (Eds.), Medical image computing and computer-assisted intervention, 2013, Part II, LNCS 8150 (pp. 649\u2013656).","DOI":"10.1007\/978-3-642-40763-5_80"},{"key":"B20","first-page":"1","author":"Zeiler M. 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