{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T10:13:06Z","timestamp":1767262386507,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,12,12]],"date-time":"2023-12-12T00:00:00Z","timestamp":1702339200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Key R&amp;D Program of China","award":["2022YFB3207600","62103154","U21A20481","2021PP15002000","ZDZX2021-4","2021XXJS097","20220819"],"award-info":[{"award-number":["2022YFB3207600","62103154","U21A20481","2021PP15002000","ZDZX2021-4","2021XXJS097","20220819"]}]},{"name":"National Natural Science Foundation of China","award":["2022YFB3207600","62103154","U21A20481","2021PP15002000","ZDZX2021-4","2021XXJS097","20220819"],"award-info":[{"award-number":["2022YFB3207600","62103154","U21A20481","2021PP15002000","ZDZX2021-4","2021XXJS097","20220819"]}]},{"name":"CCF-Baidu funding","award":["2022YFB3207600","62103154","U21A20481","2021PP15002000","ZDZX2021-4","2021XXJS097","20220819"],"award-info":[{"award-number":["2022YFB3207600","62103154","U21A20481","2021PP15002000","ZDZX2021-4","2021XXJS097","20220819"]}]},{"name":"SINOMRCH funding","award":["2022YFB3207600","62103154","U21A20481","2021PP15002000","ZDZX2021-4","2021XXJS097","20220819"],"award-info":[{"award-number":["2022YFB3207600","62103154","U21A20481","2021PP15002000","ZDZX2021-4","2021XXJS097","20220819"]}]},{"name":"HUST funding","award":["2022YFB3207600","62103154","U21A20481","2021PP15002000","ZDZX2021-4","2021XXJS097","20220819"],"award-info":[{"award-number":["2022YFB3207600","62103154","U21A20481","2021PP15002000","ZDZX2021-4","2021XXJS097","20220819"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Compressed sensing (CS) is a popular data compression theory for many computer vision tasks, but the high reconstruction complexity for images prevents it from being used in many real-world applications. Existing end-to-end learning methods achieved real time sensing but lack theory guarantee for robust reconstruction results. This paper proposes a neural network called RootsNet, which integrates the CS mechanism into the network to prevent error propagation. So, RootsNet knows what will happen if some modules in the network go wrong. It also implements real-time and successfully reconstructed extremely low measurement rates that are impossible for traditional optimization-theory-based methods. For qualitative validation, RootsNet is implemented in two real-world measurement applications, i.e., a near-field microwave imaging system and a pipeline inspection system, where RootsNet easily saves 60% more measurement time and 95% more data compared with the state-of-the-art optimization-theory-based reconstruction methods. Without losing generality, comprehensive experiments are performed on general datasets, including evaluating the key components in RootsNet, the reconstruction uncertainty, quality, and efficiency. RootsNet has the best uncertainty performance and efficiency, and achieves the best reconstruction quality under super low-measurement rates.<\/jats:p>","DOI":"10.3390\/e25121648","type":"journal-article","created":{"date-parts":[[2023,12,12]],"date-time":"2023-12-12T05:23:22Z","timestamp":1702358602000},"page":"1648","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A Real-Time and Robust Neural Network Model for Low-Measurement-Rate Compressed-Sensing Image Reconstruction"],"prefix":"10.3390","volume":"25","author":[{"given":"Pengchao","family":"Chen","sequence":"first","affiliation":[{"name":"PipeChina Institute of Science and Technology, Langfang 065000, China"}]},{"given":"Huadong","family":"Song","sequence":"additional","affiliation":[{"name":"SINOMACH Sensing Technology Co., Ltd., Shenyang 110043, China"}]},{"given":"Yanli","family":"Zeng","sequence":"additional","affiliation":[{"name":"SINOMACH Sensing Technology Co., Ltd., Shenyang 110043, China"}]},{"given":"Xiaoting","family":"Guo","sequence":"additional","affiliation":[{"name":"SINOMACH Sensing Technology Co., Ltd., Shenyang 110043, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3749-947X","authenticated-orcid":false,"given":"Chaoqing","family":"Tang","sequence":"additional","affiliation":[{"name":"China Belt and Road Joint Lab. on Measurement and Control Technology, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology (HUST), No 1037 Luoyu Rd., Wuhan 430074, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,12]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Superresolution Radar Imaging via Peak Search and Compressed Sensing","volume":"19","author":"Wu","year":"2022","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"103975","DOI":"10.1016\/j.dsp.2023.103975","article-title":"Compressed sensing based on L1 and TGV regularization for low-light-level images denoising","volume":"136","author":"Cui","year":"2023","journal-title":"Digit. Signal Process."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"36516","DOI":"10.1109\/ACCESS.2019.2903826","article-title":"Secure Remote Sensing Image Registration Based on Compressed Sensing in Cloud Setting","volume":"7","author":"Liu","year":"2019","journal-title":"IEEE Access"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"947","DOI":"10.1109\/TIM.2020.2970832","article-title":"Compressive-Sensing-Based Reflectometer for Sparse-Fault Detection in Elevator Belts","volume":"69","author":"Oya","year":"2020","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1109\/TIM.2017.2759418","article-title":"Intelligent Bearing Fault Diagnosis Method Combining Compressed Data Acquisition and Deep Learning","volume":"67","author":"Sun","year":"2018","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"9608","DOI":"10.1109\/TIE.2017.2698406","article-title":"Smart Compressed Sensing for Online Evaluation of CFRP Structure Integrity","volume":"64","author":"Tang","year":"2017","journal-title":"IEEE Trans. Ind. Electron."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TIM.2020.3047503","article-title":"Structure-Aware Compressive Sensing for Magnetic Flux Leakage Detectors: Theory and Experimental Validation","volume":"70","author":"Najafabadi","year":"2021","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"4722","DOI":"10.1109\/TIM.2019.2951891","article-title":"Compressed Sensing Method for Health Monitoring of Pipelines Based on Guided Wave Inspection","volume":"69","author":"Wang","year":"2020","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1109\/TIT.2005.862083","article-title":"Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information","volume":"52","author":"Romberg","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1109\/TCI.2018.2846413","article-title":"Convolutional Neural Networks for Noniterative Reconstruction of Compressively Sensed Images","volume":"4","author":"Lohit","year":"2018","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1109\/TCSVT.2020.2978703","article-title":"Video Compressed Sensing Using a Convolutional Neural Network","volume":"31","author":"Shi","year":"2021","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1038\/nature14539","article-title":"Deep learning","volume":"521","author":"LeCun","year":"2015","journal-title":"Nature"},{"key":"ref_13","unstructured":"Kulkarni, K., Lohit, S., Turaga, P., Kerviche, R., and Ashok, A. (2021, January 20\u201325). Reconnet: Non-iterative reconstruction of images from compressively sensed measurements. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Nashville, TN, USA."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"158695","DOI":"10.1109\/ACCESS.2021.3130973","article-title":"GPX-ADMM-Net: Interpretable Deep Neural Network for Image Compressive Sensing","volume":"9","author":"Hu","year":"2021","journal-title":"IEEE Access"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Seong, J.T. (2018, January 24\u201327). Review on non-iterative recovery frameworks in compressed sensing. Proceedings of the 2018 International Conference on Electronics, Information, and Communication (ICEIC), Honolulu, HI, USA.","DOI":"10.23919\/ELINFOCOM.2018.8330668"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1109\/TIP.2019.2928136","article-title":"Image compressed sensing using convolutional neural network","volume":"29","author":"Shi","year":"2019","journal-title":"IEEE Trans. Image Process."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Shi, W., Jiang, F., and Liu, S. (2019, January 15\u201320). Scalable convolutional neural network for image compressed sensing. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition, Long Beach, CA, USA.","DOI":"10.1109\/CVPR.2019.01257"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1109\/TRPMS.2020.2991877","article-title":"MD-recon-net: A parallel dual-domain convolutional neural network for compressed sensing MRI","volume":"5","author":"Ran","year":"2020","journal-title":"IEEE Trans. Radiat. Plasma Med. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3405","DOI":"10.1109\/TIM.2015.2459471","article-title":"Compressed Sensing: A Simple Deterministic Measurement Matrix and a Fast Recovery Algorithm","volume":"64","author":"Ravelomanantsoa","year":"2015","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Zhang, J., and Ghanem, B. (2018, January 18\u201323). ISTA-Net: Interpretable optimization-inspired deep network for image compressive sensing. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00196"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"6066","DOI":"10.1109\/TIP.2021.3091834","article-title":"Coast: Controllable arbitrary-sampling network for compressive sensing","volume":"30","author":"You","year":"2021","journal-title":"IEEE Trans. Image Process."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"You, D., Xie, J., and Zhang, J. (2021, January 5\u20139). ISTA-Net++: Flexible deep unfolding network for compressive sensing. Proceedings of the 2021 IEEE International Conference on Multimedia and Expo (ICME), Shenzhen, China.","DOI":"10.1109\/ICME51207.2021.9428249"},{"key":"ref_23","first-page":"1","article-title":"Deep ADMM-Net for compressive sensing MRI","volume":"29","author":"Sun","year":"2016","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1109\/TPAMI.2018.2883941","article-title":"ADMM-CSNet: A deep learning approach for image compressive sensing","volume":"42","author":"Yang","year":"2018","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"47943","DOI":"10.1109\/ACCESS.2018.2867435","article-title":"Co-robust-ADMM-net: Joint ADMM framework and DNN for robust sparse composite regularization","volume":"6","author":"Li","year":"2018","journal-title":"IEEE Access"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1487","DOI":"10.1109\/TIP.2020.3044472","article-title":"AMP-Net: Denoising-based deep unfolding for compressive image sensing","volume":"30","author":"Zhang","year":"2020","journal-title":"IEEE Trans. Image Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3027","DOI":"10.1109\/JIOT.2020.3021724","article-title":"Deep Unfolding With Weighted \u21132 Minimization for Compressive Sensing","volume":"8","author":"Zhang","year":"2020","journal-title":"IEEE Internet Things J."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1109\/TCI.2016.2629286","article-title":"Plug-and-play ADMM for image restoration: Fixed-point convergence and applications","volume":"3","author":"Chan","year":"2016","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"458","DOI":"10.1109\/JETCAS.2020.3039731","article-title":"Deep Neural Oracle With Support Identification in the Compressed Domain","volume":"10","author":"Prono","year":"2020","journal-title":"IEEE J. Emerg. Sel. Top. Circuits Syst."},{"key":"ref_30","unstructured":"Wu, Y., Rosca, M., and Lillicrap, T. (2019, January 10\u201315). Deep compressed sensing. Proceedings of the International Conference on Machine Learning, Long Beach, CA, USA."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1109\/JSTSP.2020.2977507","article-title":"Optimization-inspired compact deep compressive sensing","volume":"14","author":"Zhang","year":"2020","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"5117","DOI":"10.1109\/TIT.2016.2556683","article-title":"From denoising to compressed sensing","volume":"62","author":"Metzler","year":"2016","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"022137","DOI":"10.1103\/PhysRevE.94.022137","article-title":"Bayesian online compressed sensing","volume":"94","author":"Rossi","year":"2016","journal-title":"Phys. Rev. E"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"5287","DOI":"10.1109\/TIM.2019.2962562","article-title":"Feature-Supervised Compressed Sensing for Microwave Imaging Systems","volume":"69","author":"Tang","year":"2020","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"2528","DOI":"10.1109\/TMECH.2020.3041768","article-title":"Segmentation-oriented Compressed Sensing for Efficient Impact Damage Detection on CFRP Materials","volume":"26","author":"Tang","year":"2021","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1148","DOI":"10.1109\/TCI.2021.3122285","article-title":"Deep coded aperture design: An end-to-end approach for computational imaging tasks","volume":"7","author":"Bacca","year":"2021","journal-title":"IEEE Trans. Comput. Imaging"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"7338","DOI":"10.1109\/TII.2021.3050146","article-title":"Model-Assisted Compressed Sensing for Vibration-Based Structural Health Monitoring","volume":"17","author":"Zonzini","year":"2021","journal-title":"IEEE Trans. Ind. Inf."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1207","DOI":"10.1002\/cpa.20124","article-title":"Stable signal recovery from incomplete and inaccurate measurements","volume":"59","author":"Romberg","year":"2006","journal-title":"Commun. Pure Appl. Math."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"K\u00fcng, R., and Jung, P. (2016, January 11\u201314). Robust nonnegative sparse recovery and 0\/1-Bernoulli measurements. Proceedings of the 2016 IEEE Information Theory Workshop (ITW), Cambridge, UK.","DOI":"10.1109\/ITW.2016.7606836"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"4680","DOI":"10.1109\/TIT.2011.2146090","article-title":"Orthogonal matching pursuit for sparse signal recovery with noise","volume":"57","author":"Cai","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"25267","DOI":"10.1109\/JSEN.2021.3071151","article-title":"The Compressed Sensing of Wireless Sensor Networks Based on Internet of Things","volume":"21","author":"Wei","year":"2021","journal-title":"IEEE Sens. J."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"898","DOI":"10.1109\/TPAMI.2010.161","article-title":"Contour detection and hierarchical image segmentation","volume":"33","author":"Arbelaez","year":"2010","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"600","DOI":"10.1109\/TIP.2003.819861","article-title":"Image quality assessment: From error visibility to structural similarity","volume":"13","author":"Wang","year":"2004","journal-title":"IEEE Trans. Image Process."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"58869","DOI":"10.1109\/ACCESS.2022.3179517","article-title":"A Review of Wavelet Analysis and Its Applications: Challenges and Opportunities","volume":"10","author":"Guo","year":"2022","journal-title":"IEEE Access"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1006\/jath.2000.3514","article-title":"On the Construction and Frequency Localization of Finite Orthogonal Quadrature Filters","volume":"108","author":"Nielsen","year":"2001","journal-title":"J. Approx. Theory"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1109\/JSTSP.2010.2042411","article-title":"Normalized iterative hard thresholding: Guaranteed stability and performance","volume":"4","author":"Blumensath","year":"2010","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"2479","DOI":"10.1109\/TSP.2009.2016892","article-title":"Sparse reconstruction by separable approximation","volume":"57","author":"Wright","year":"2009","journal-title":"IEEE Trans. Signal Process."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/12\/1648\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:37:17Z","timestamp":1760132237000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/12\/1648"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,12]]},"references-count":47,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2023,12]]}},"alternative-id":["e25121648"],"URL":"https:\/\/doi.org\/10.3390\/e25121648","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2023,12,12]]}}}