{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:42:55Z","timestamp":1760240575191,"version":"build-2065373602"},"reference-count":33,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2019,8,5]],"date-time":"2019-08-05T00:00:00Z","timestamp":1564963200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation for Excellent Young Scholars of China","award":["41722405"],"award-info":[{"award-number":["41722405"]}]},{"name":"National Key Foundation for Exploring Scientific Instrument of China","award":["2017YFC0804105"],"award-info":[{"award-number":["2017YFC0804105"]}]},{"name":"Key Research and Development Program of Jilin Province of China","award":["20180201017GX, 20160414002GH"],"award-info":[{"award-number":["20180201017GX, 20160414002GH"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>The magnetic resonance sounding (MRS) method is a non-invasive, efficient and advanced geophysical method for groundwater detection. However, the MRS signal received by the coil sensor is extremely susceptible to electromagnetic noise interference. In MRS data processing, random noise suppression of noisy MRS data is an important research aspect. We propose an approach for intensive sampling sparse reconstruction (ISSR) and kernel regression estimation (KRE) to suppress random noise. The approach is based on variable frequency sampling, numerical integration and statistical signal processing combined with kernel regression estimation. In order to realize the approach, we proposed three specific sparse reconstructions, namely rectangular sparse reconstruction, trapezoidal sparse reconstruction and Simpson sparse reconstruction. To solve the distortion of peaks and valleys after sparse reconstruction, we introduced the KRE to deal with the processed data by the ISSR. Further, the simulation and field experiments demonstrate that the ISSR-KRE approach is a feasible and effective way to suppress random noise. Besides, we find that rectangular sparse reconstruction and trapezoidal sparse reconstruction are superior to Simpson sparse reconstruction in terms of noise suppression effect, and sampling frequency is positively correlated with signal-to-noise improvement ratio (SNIR). In one case of field experiment, the standard deviation of noisy MRS data was reduced from 1200.80 nV to 570.01 nV by the ISSR-KRE approach. The proposed approach provides theoretical support for random noise suppression and contributes to the development of MRS instrument with low power consumption and high efficiency. In the future, we will integrate the approach into MRS instrument and attempt to utilize them to eliminate harmonic noise from power line.<\/jats:p>","DOI":"10.3390\/rs11151829","type":"journal-article","created":{"date-parts":[[2019,8,5]],"date-time":"2019-08-05T11:17:47Z","timestamp":1565003867000},"page":"1829","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Random Noise Suppression of Magnetic Resonance Sounding Data with Intensive Sampling Sparse Reconstruction and Kernel Regression Estimation"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5189-5786","authenticated-orcid":false,"given":"Xiaokang","family":"Yao","sequence":"first","affiliation":[{"name":"College of Instrumentation and Electrical Engineering, Jilin University, Changchun 130061, China"},{"name":"Key Laboratory of Geo-exploration Instruments, Ministry of Education of China, Changchun 130061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianmin","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Geo-exploration Instruments, Ministry of Education of China, Changchun 130061, China"},{"name":"College of Geo-Exploration Science and Technology, Jilin University, Changchun 130026, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhenyang","family":"Yu","sequence":"additional","affiliation":[{"name":"College of Instrumentation and Electrical Engineering, Jilin University, Changchun 130061, China"},{"name":"Key Laboratory of Geo-exploration Instruments, Ministry of Education of China, Changchun 130061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fa","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Instrumentation and Electrical Engineering, Jilin University, Changchun 130061, China"},{"name":"Key Laboratory of Geo-exploration Instruments, Ministry of Education of China, Changchun 130061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yong","family":"Sun","sequence":"additional","affiliation":[{"name":"College of Instrumentation and Electrical Engineering, Jilin University, Changchun 130061, China"},{"name":"Key Laboratory of Geo-exploration Instruments, Ministry of Education of China, Changchun 130061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3752","DOI":"10.1109\/TGRS.2007.903829","article-title":"Surface nuclear magnetic resonance tomography","volume":"45","author":"Hertrich","year":"2007","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1016\/S0926-9851(03)00041-7","article-title":"Removal of power-line harmonics from proton magnetic resonance measurements","volume":"53","author":"Legchenko","year":"2003","journal-title":"J. Appl. Geophys."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1109\/LGRS.2017.2772790","article-title":"Removal of Co-Frequency Powerline Harmonics from Multichannel Surface NMR Data","volume":"15","author":"Liu","year":"2018","journal-title":"IEEE Geosci. Remote Sens. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Chen, H.M., Wang, H.C., Chai, J.W., Chen, C.C.C., Xue, B., Wang, L., Yu, C., Wang, Y., Song, M., and Chang, C.I. (2017). A Hyperspectral Imaging Approach to White Matter Hyperintensities Detection in Brain Magnetic Resonance Images. Remote Sens., 9.","DOI":"10.3390\/rs9111174"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Powers, J.M., Ioachim, G., and Stroman, P.W. (2018). Ten Key Insights into the Use of Spinal Cord fMRI. Brain Sci., 8.","DOI":"10.3390\/brainsci8090173"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1111\/j.1745-6584.2006.00198.x","article-title":"Resolution of MRS applied to the characterization of hard-rock aquifers","volume":"44","author":"Legchenko","year":"2006","journal-title":"Groundwater"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1016\/j.jappgeo.2008.03.006","article-title":"Multi-channel surface NMR instrumentation and software for 1D\/2D groundwater investigations","volume":"66","author":"Walsh","year":"2008","journal-title":"J. Appl. Geophys."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Qin, S., Ma, Z., Jiang, C., Lin, J., Xue, Y., Shang, X., and Li, Z. (2017). Response Characteristics and Experimental Study of Underground Magnetic Resonance Sounding Using a Small-Coil Sensor. Sensors, 17.","DOI":"10.3390\/s17092127"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1187","DOI":"10.1007\/s10040-018-1726-1","article-title":"Mapping groundwater reserves in northwestern Cambodia with the combined use of data from lithologs and time-domain-electromagnetic and magnetic-resonance soundings","volume":"26","author":"Valois","year":"2018","journal-title":"Hydrogeol. J."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"EN33","DOI":"10.1190\/geo2018-0563.1","article-title":"Surface nuclear magnetic resonance observations of permafrost thaw below floating, bedfast and transitional ice lakes","volume":"84","author":"Parsekian","year":"2019","journal-title":"Geophysics"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"WA131","DOI":"10.1190\/geo2015-0125.1","article-title":"Ground-penetrating radar and surface nuclear magnetic resonance monitoring of an englacial water-filled cavity in the polythermal glacier of Tete Rousse","volume":"81","author":"Garambois","year":"2016","journal-title":"Geophysics"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Shang, X., Jiang, C., Ma, Z., and Qin, S. (2018). Combined System of Magnetic Resonance Sounding and Time-Domain Electromagnetic Method for Water-Induced Disaster Detection in Tunnels. Sensors, 18.","DOI":"10.3390\/s18103508"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"WB97","DOI":"10.1190\/geo2015-0386.1","article-title":"Algorithms for removing surface water signals from surface nuclear magnetic resonance infiltration surveys","volume":"81","author":"Falzone","year":"2016","journal-title":"Geophysics"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1111\/1365-2478.12296","article-title":"Surface nuclear magnetic resonance signals recovery by integration of a non-linear decomposition method with statistical analysis","volume":"64","author":"Ghanati","year":"2016","journal-title":"Geophys. Prospect."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"894","DOI":"10.1093\/gji\/ggz068","article-title":"Complex envelope retrieval for surface nuclear magnetic resonance data using spectral analysis","volume":"217","author":"Liu","year":"2019","journal-title":"Geophys. J. Int."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"459","DOI":"10.3997\/1873-0604.2011026","article-title":"Statistical stacking and adaptive notch filter to remove high-level electromagnetic noise from MRS measurements","volume":"9","author":"Jiang","year":"2011","journal-title":"Near Surf. Geophys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"WB1","DOI":"10.1190\/geo2015-0442.1","article-title":"Model-based subtraction of spikes from surface nuclear magnetic resonance data","volume":"81","author":"Larsen","year":"2016","journal-title":"Geophysics"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"828","DOI":"10.1093\/gji\/ggt422","article-title":"Noise cancelling of MRS signals combining model-based removal of powerline harmonics and multichannel Wiener filtering","volume":"196","author":"Larsen","year":"2014","journal-title":"Geophys. J. Int."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1962","DOI":"10.1093\/gji\/ggy389","article-title":"An alternative approach to handling co-frequency harmonics in surface nuclear magnetic resonance data","volume":"215","author":"Wang","year":"2018","journal-title":"Geophys. J. Int."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.jappgeo.2014.08.009","article-title":"A temporal and spatial analysis of anthropogenic noise sources affecting SNMR","volume":"110","author":"Dalgaard","year":"2014","journal-title":"J. Appl. Geophys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/S0926-9851(98)00011-1","article-title":"Processing of surface proton magnetic resonance signals using non-linear fitting","volume":"39","author":"Legchenko","year":"1998","journal-title":"J. Appl. Geophys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1111\/j.1365-246X.2012.05618.x","article-title":"Adaptive noise cancelling of multichannel magnetic resonance sounding signals","volume":"191","author":"Dalgaard","year":"2012","journal-title":"Geophys. J. Int."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1016\/j.jappgeo.2016.04.005","article-title":"Filtering and parameter estimation of surface-NMR data using singular spectrum analysis","volume":"130","author":"Ghanati","year":"2016","journal-title":"J. Appl. Geophys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"727","DOI":"10.1093\/gji\/ggy001","article-title":"Time-frequency peak filtering for random noise attenuation of magnetic resonance sounding signal","volume":"213","author":"Lin","year":"2018","journal-title":"Geophys. J. Int."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"855","DOI":"10.1111\/j.1365-2478.1994.tb00245.x","article-title":"The potential of a noise-reducing antenna for surface NMR groundwater surveys in the Earth\u2019s magnetic field","volume":"42","author":"Trushkin","year":"1994","journal-title":"Geophys. Prospect."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1093\/gji\/ggw004","article-title":"Increasing the resolution and the signal-to-noise ratio of magnetic resonance sounding data using a central loop configuration","volume":"205","author":"Behroozmand","year":"2016","journal-title":"Geophys. J. Int."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Karine, A., Toumi, A., Khenchaf, A., and El Hassouni, M. (2018). Radar Target Recognition Using Salient Keypoint Descriptors and Multitask Sparse Representation. Remote Sens., 10.","DOI":"10.20944\/preprints201804.0251.v1"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Zhang, J., Zeng, Z., Zhang, L., Lu, Q., and Wang, K. (2019). Application of Mathematical Morphological Filtering to Improve the Resolution of Chang\u2019E-3 Lunar Penetrating Radar Data. Remote Sens., 11.","DOI":"10.3390\/rs11050524"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1109\/TIP.2006.888330","article-title":"Kernel Regression for Image Processing and Reconstruction","volume":"16","author":"Takeda","year":"2007","journal-title":"IEEE Trans. Image Process."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Legchenko, A. (2013). Magnetic Resonance Imaging for Groundwater, ISTE Ltd.","DOI":"10.1002\/9781118649459"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/S0926-9851(02)00127-1","article-title":"A review of the basic principles for proton magnetic resonance sounding measurements","volume":"50","author":"Legchenko","year":"2002","journal-title":"J. Appl. Geophys."},{"key":"ref_32","unstructured":"Li, Q., Wang, N., and Yi, D. (2008). Numerical Analysis, Tsinghua University Press. [5th ed.]."},{"key":"ref_33","unstructured":"Sheng, Z., Xie, S., and Pan, C. (2008). Probability Theory and Mathematical Statistics, Higher Education Press. [4th ed.]."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/15\/1829\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:08:47Z","timestamp":1760188127000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/11\/15\/1829"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,5]]},"references-count":33,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2019,8]]}},"alternative-id":["rs11151829"],"URL":"https:\/\/doi.org\/10.3390\/rs11151829","relation":{},"ISSN":["2072-4292"],"issn-type":[{"type":"electronic","value":"2072-4292"}],"subject":[],"published":{"date-parts":[[2019,8,5]]}}}