{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T21:03:56Z","timestamp":1778965436766,"version":"3.51.4"},"reference-count":39,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,13]],"date-time":"2022-07-13T00:00:00Z","timestamp":1657670400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key Research and Development Project of China","award":["2020YFC1522002"],"award-info":[{"award-number":["2020YFC1522002"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The resolution of 3D structure reconstructed by laboratory nanoCT is often affected by changes in ambient temperature. Although correction methods based on projection alignment have been widely used, they are time-consuming and complex. Especially in piecewise samples (e.g., chips), the existing methods are semi-automatic because the projections lose attenuation information at some rotation angles. Herein, we propose a fast correction method that directly processes the reconstructed slices. Thus, the limitations of the existing methods are addressed. The method is named multiscale dense U-Net (MD-Unet), which is based on MIMO-Unet and achieves state-of-the-art artifacts correction performance in nanoCT. Experiments show that MD-Unet can significantly boost the correction performance (e.g., with three orders of magnitude improvement in correction speed compared with traditional methods), and MD-Unet+ improves 0.92 dB compared with MIMO-Unet in the chip dataset.<\/jats:p>","DOI":"10.3390\/e24070967","type":"journal-article","created":{"date-parts":[[2022,7,13]],"date-time":"2022-07-13T22:06:00Z","timestamp":1657749960000},"page":"967","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Multiscale Dense U-Net: A Fast Correction Method for Thermal Drift Artifacts in Laboratory NanoCT Scans of Semi-Conductor Chips"],"prefix":"10.3390","volume":"24","author":[{"given":"Mengnan","family":"Liu","sequence":"first","affiliation":[{"name":"Henan Key Laboratory of Imaging and Intelligent Processing, PLA Strategic Support Force Information Engineering University, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yu","family":"Han","sequence":"additional","affiliation":[{"name":"Henan Key Laboratory of Imaging and Intelligent Processing, PLA Strategic Support Force Information Engineering University, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoqi","family":"Xi","sequence":"additional","affiliation":[{"name":"Henan Key Laboratory of Imaging and Intelligent Processing, PLA Strategic Support Force Information Engineering University, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Linlin","family":"Zhu","sequence":"additional","affiliation":[{"name":"Henan Key Laboratory of Imaging and Intelligent Processing, PLA Strategic Support Force Information Engineering University, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuangzhan","family":"Yang","sequence":"additional","affiliation":[{"name":"Henan Key Laboratory of Imaging and Intelligent Processing, PLA Strategic Support Force Information Engineering University, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Siyu","family":"Tan","sequence":"additional","affiliation":[{"name":"Henan Key Laboratory of Imaging and Intelligent Processing, PLA Strategic Support Force Information Engineering University, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jian","family":"Chen","sequence":"additional","affiliation":[{"name":"Henan Key Laboratory of Imaging and Intelligent Processing, PLA Strategic Support Force Information Engineering University, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lei","family":"Li","sequence":"additional","affiliation":[{"name":"Henan Key Laboratory of Imaging and Intelligent Processing, PLA Strategic Support Force Information Engineering University, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bin","family":"Yan","sequence":"additional","affiliation":[{"name":"Henan Key Laboratory of Imaging and Intelligent Processing, PLA Strategic Support Force Information Engineering University, Zhengzhou 450001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1055\/s-0041-106541","article-title":"Nano-Computed Tomography: Technique and Applications","volume":"188","author":"Kampschulte","year":"2016","journal-title":"RoFo Fortschritte Gebiete Rontgenstrahlen Nuklearmedizin"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Langheinrich, A.C., Yeniguen, M., Ostendorf, A., Marhoffer, S., Kampschulte, M., Bachmann, G., Stolz, E., and Gerriets, T. (2010). Evaluation of the middle cerebral artery occlusion techniques in the rat by in-vitro 3-dimensional micro- and nano computed tomography. BMC Neurol., 10.","DOI":"10.1186\/1471-2377-10-36"},{"key":"ref_3","first-page":"1","article-title":"Artificial neural network approach for multiphase segmentation of battery electrode nano-CT images","volume":"8","author":"Su","year":"2022","journal-title":"NPJ Comput. Math."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"012018","DOI":"10.1088\/1742-6596\/849\/1\/012018","article-title":"Understanding transport phenomena in electrochemical energy devices via X-ray nano CT","volume":"849","author":"Tjaden","year":"2017","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"C01029","DOI":"10.1088\/1748-0221\/11\/01\/C01029","article-title":"Correction of the X-ray tube spot movement as a tool for improvement of the micro-tomography quality","volume":"11","author":"Vavrik","year":"2016","journal-title":"J. Instrum."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"327","DOI":"10.4028\/www.scientific.net\/KEM.613.327","article-title":"Characterization and Correction of Geometric Errors Induced by Thermal Drift in CT Measurements","volume":"613","author":"Porath","year":"2014","journal-title":"Key Eng. Mater."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"21345","DOI":"10.1364\/OE.19.021345","article-title":"Phase tomography from x-ray coherent diffractive imaging projections","volume":"19","author":"Diaz","year":"2011","journal-title":"Opt. Express"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"36637","DOI":"10.1364\/OE.27.036637","article-title":"Alignment methods for nanotomography with deep subpixel accuracy","volume":"27","author":"Holler","year":"2019","journal-title":"Opt. Express"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"70781C","DOI":"10.1117\/12.793212","article-title":"Compensation of mechanical inaccuracies in micro-CT and nano-CT","volume":"7078","author":"Sasov","year":"2008","journal-title":"Proc SPIE"},{"key":"ref_10","first-page":"161","article-title":"A post-scan method for correcting artefacts of slow geometry changes during micro-tomographic scans","volume":"17","author":"Salmon","year":"2009","journal-title":"J. X-Ray Sci. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"085404","DOI":"10.1088\/0957-0233\/23\/8\/085404","article-title":"Physical characterization and performance evaluation of an x-ray micro-computed tomography system for dimensional metrology applications","volume":"23","author":"Hiller","year":"2012","journal-title":"Meas. Sci. Technol."},{"key":"ref_12","unstructured":"Vogeler, F., Verheecke, W., Voet, A., Kruth, J.P., and Dewulf, W. (2011, January 20\u201322). Positional Stability of 2D X-ray Images for Computer Tomography. Proceedings of the International Symposium on Digital Industrial Radiology and Computed Tomography (DIR 2011), Berlin, Germany."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Liu, M., Han, Y., Xi, X., Tan, S., Chen, J., Li, L., and Yan, B. (2021). Thermal Drift Correction for Laboratory Nano Computed Tomography via Outlier Elimination and Feature Point Adjustment. Sensors, 21.","DOI":"10.3390\/s21248493"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"11818","DOI":"10.1038\/s41598-017-12141-9","article-title":"Rapid alignment of nanotomography data using joint iterative reconstruction and reprojection","volume":"7","author":"Hong","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1107\/S1600577518015242","article-title":"Nanoporous gold: A hierarchical and multiscale 3D test pattern for characterizing X-ray nano-tomography systems","volume":"26","author":"Larsson","year":"2019","journal-title":"J. Synchrotron Radiat."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1909","DOI":"10.1107\/S1600577521008481","article-title":"Deep-learning-based image registration for nano-resolution tomographic reconstruction","volume":"28","author":"Fu","year":"2021","journal-title":"J. Synchrotron Radiat."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Liu, M., Han, Y., Xi, X., Zhu, M., Zhu, L., Song, X., Kang, G., Yang, S., Li, L., and Yan, B. (2021). Horizontal Drift Correction by Trajectory of Sinogram Centroid Fitting for Laboratory X-ray Nanotomography, ICOIP.","DOI":"10.1117\/12.2605873"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1109\/TCI.2021.3060915","article-title":"Distributed Optimization for Nonrigid Nano-Tomography","volume":"7","author":"Nikitin","year":"2021","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Cho, S.J., Ji, S.W., Hong, J.P., Jung, S.W., and Ko, S.J. (2021). Rethinking Coarse-to-Fine Approach in Single Image Deblurring. arXiv.","DOI":"10.1109\/ICCV48922.2021.00460"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Nah, S., Kim, T.H., and Lee, K.M. (2016). Deep Multi-Scale Convolutional Neural Network for Dynamic Scene Deblurring, Computer Society.","DOI":"10.1109\/CVPR.2017.35"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"612","DOI":"10.1364\/JOSAA.1.000612","article-title":"Practical cone-beam algorithm","volume":"1","author":"Feldkamp","year":"1984","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1109\/TMI.2021.3111679","article-title":"Genetic U-Net: Automatically Designed Deep Networks for Retinal Vessel Segmentation Using a Genetic Algorithm","volume":"41","author":"Wei","year":"2022","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1111\/j.1477-9730.1984.tb00505.x","article-title":"digital image correlation: Performance and potential application in photogrammetry","volume":"11","author":"Ackermann","year":"2006","journal-title":"Photogramm. Rec."},{"key":"ref_24","first-page":"1858","article-title":"Parametric image alignment using enhanced correlation coefficient maximization","volume":"31","author":"Georgios","year":"2008","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1364\/OL.33.000156","article-title":"Efficient subpixel image registration algorithms","volume":"33","author":"Fienup","year":"2008","journal-title":"Opt. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1016\/j.cviu.2007.09.014","article-title":"Speeded-Up Robust Features (SURF)","volume":"110","author":"Bay","year":"2008","journal-title":"Comput. Vis. Image Underst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"512","DOI":"10.1007\/s11263-018-1117-z","article-title":"Locality Preserving Matching","volume":"127","author":"Ma","year":"2019","journal-title":"Int. J. Comput. Vis."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1006\/cviu.1999.0832","article-title":"MLESAC: A New Robust Estimator with Application to Estimating Image Geometry","volume":"78","author":"Torr","year":"2000","journal-title":"Comput. Vis. Image Underst."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Tao, X., Gao, H., Wang, Y., Shen, X., Wang, J., and Jia, J. (2018, January 18\u201323). Scale-recurrent Network for Deep Image Deblurring. Proceedings of the 2018 IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00853"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Kupyn, O., Martyniuk, T., Wu, J., and Wang, Z. (2019, January 15\u201320). DeblurGAN-v2: Deblurring (Orders-of-Magnitude) Faster and Better. Proceedings of the 2018 IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Long Beach, CA, USA.","DOI":"10.1109\/ICCV.2019.00897"},{"key":"ref_31","unstructured":"Wu, H., Ni, N., and Zhang, L. (2021). Scale-Aware Dynamic Network for Continuous-Scale Super-Resolution. arXiv."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Li, J., Fang, F., Mei, K., and Zhang, G. (2018, January 8\u201312). Multi-scale Residual Network for Image Super-Resolution. Proceedings of the ECCV, Munich, Germany.","DOI":"10.1007\/978-3-030-01237-3_32"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3726","DOI":"10.1109\/TIP.2022.3175432","article-title":"DO-Conv: Depthwise Over-parameterized Convolutional Layer","volume":"31","author":"Cao","year":"2020","journal-title":"IEEE Trans. Image Processing"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Tian, Y., Kong, Y., Zhong, B., and Fu, Y. (2018, January 18\u201323). Residual Dense Network for Image Super-Resolution. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00262"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Li, K., Li, K., Wang, L., Zhong, B., and Fu, Y. (2018, January 8\u201312). Image Super-Resolution Using Very Deep Residual Channel Attention Networks. Proceedings of the ECCV, Munich, Germany.","DOI":"10.1007\/978-3-030-01234-2_18"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Lim, B., Son, S., Kim, H., Nah, S., and Lee, K.M. (2017, January 21\u201326). Enhanced Deep Residual Networks for Single Image Super-Resolution. Proceedings of the 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Honolulu, HI, USA.","DOI":"10.1109\/CVPRW.2017.151"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Wang, X., Yu, K., Wu, S., Gu, J., Liu, Y., Dong, C., Loy, C.C., Qiao, Y., and Tang, X. (2018). ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks, Springer.","DOI":"10.1007\/978-3-030-11021-5_5"},{"key":"ref_38","unstructured":"Mao, X., Liu, Y., Shen, W., Li, Q., and Wang, Y. (2021). Deep Residual Fourier Transformation for Single Image Deblurring. arXiv."},{"key":"ref_39","unstructured":"Xin, J., Liang, L., Le, S., and Chen, Z. (2012). Improved total variation based CT reconstruction algorithm with noise estimation. Spie Optical Engineering + Applications, SPIE."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/7\/967\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:49:29Z","timestamp":1760140169000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/7\/967"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,13]]},"references-count":39,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2022,7]]}},"alternative-id":["e24070967"],"URL":"https:\/\/doi.org\/10.3390\/e24070967","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7,13]]}}}