{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T23:22:51Z","timestamp":1784676171933,"version":"3.55.0"},"reference-count":65,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,12,28]],"date-time":"2021-12-28T00:00:00Z","timestamp":1640649600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Lossy compression of remote sensing data has found numerous applications. Several requirements are usually imposed on methods and algorithms to be used. A large compression ratio has to be provided, introduced distortions should not lead to sufficient reduction of classification accuracy, compression has to be realized quickly enough, etc. An additional requirement could be to provide privacy of compressed data. In this paper, we show that these requirements can be easily and effectively realized by compression based on discrete atomic transform (DAT). Three-channel remote sensing (RS) images that are part of multispectral data are used as examples. It is demonstrated that the quality of images compressed by DAT can be varied and controlled by setting maximal absolute deviation. This parameter also strictly relates to more traditional metrics as root mean square error (RMSE) and peak signal-to-noise ratio (PSNR) that can be controlled. It is also shown that there are several variants of DAT having different depths. Their performances are compared from different viewpoints, and the recommendations of transform depth are given. Effects of lossy compression on three-channel image classification using the maximum likelihood (ML) approach are studied. It is shown that the total probability of correct classification remains almost the same for a wide range of distortions introduced by lossy compression, although some variations of correct classification probabilities take place for particular classes depending on peculiarities of feature distributions. Experiments are carried out for multispectral Sentinel images of different complexities.<\/jats:p>","DOI":"10.3390\/rs14010125","type":"journal-article","created":{"date-parts":[[2021,12,29]],"date-time":"2021-12-29T02:31:27Z","timestamp":1640745087000},"page":"125","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":23,"title":["Discrete Atomic Transform-Based Lossy Compression of Three-Channel Remote Sensing Images with Quality Control"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1481-9132","authenticated-orcid":false,"given":"Victor","family":"Makarichev","sequence":"first","affiliation":[{"name":"Department of Information-Communication Technologies, National Aerospace University, 61070 Kharkiv, Ukraine"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Irina","family":"Vasilyeva","sequence":"additional","affiliation":[{"name":"Department of Information-Communication Technologies, National Aerospace University, 61070 Kharkiv, Ukraine"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vladimir","family":"Lukin","sequence":"additional","affiliation":[{"name":"Department of Information-Communication Technologies, National Aerospace University, 61070 Kharkiv, Ukraine"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1920-2847","authenticated-orcid":false,"given":"Benoit","family":"Vozel","sequence":"additional","affiliation":[{"name":"Institut d\u2019Electronique et des Technologies du num\u00e9Rique, IETR UMR CNRS 6164, University of Rennes 1, 22300 Lannion, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrii","family":"Shelestov","sequence":"additional","affiliation":[{"name":"Department of Mathematical Modelling and Data Analysis, National Technical University of Ukraine \u201cIgor Sikorsky Kyiv Polytechnic Institute\u201d, 03056 Kyiv, Ukraine"},{"name":"Department of Space Information Technologies and Systems, Space Research Institute of National Academy of Sciences of Ukraine and State Space Agency of Ukraine, 03187 Kyiv, Ukraine"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9704-9702","authenticated-orcid":false,"given":"Nataliia","family":"Kussul","sequence":"additional","affiliation":[{"name":"Department of Mathematical Modelling and Data Analysis, National Technical University of Ukraine \u201cIgor Sikorsky Kyiv Polytechnic Institute\u201d, 03056 Kyiv, Ukraine"},{"name":"Department of Space Information Technologies and Systems, Space Research Institute of National Academy of Sciences of Ukraine and State Space Agency of Ukraine, 03187 Kyiv, Ukraine"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Swarnalatha, P., and Sevugan, P. (2018). New Computational Models for Image Remote Sensing and Big Data. Big Data Analytics for Satellite Image Processing and Remote Sensing, IGI Global.","DOI":"10.4018\/978-1-5225-3643-7"},{"key":"ref_2","first-page":"93","article-title":"Potential Applications of the Sentinel-2 Multispectral Sensor and the ENMAP hyperspectral Sensor in Mineral Exploration","volume":"13","author":"Mielke","year":"2014","journal-title":"EARSeL Eproc."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Joshi, N., Baumann, M., Ehammer, A., Fensholt, R., Grogan, K., Hostert, P., Jepsen, M.R., Kuemmerle, T., Meyfroidt, P., and Mitchard, E.T.A. (2016). A Review of the Application of Optical and Radar Remote Sensing Data Fusion to Land Use Mapping and Monitoring. Remote Sens., 8.","DOI":"10.3390\/rs8010070"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1080\/17538947.2019.1610807","article-title":"A workflow for Sustainable Development Goals indicators assessment based on high-resolution satellite data","volume":"13","author":"Kussul","year":"2020","journal-title":"Int. J. Digit. Earth"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"39","DOI":"10.5194\/isprsarchives-XL-7-W3-39-2015","article-title":"Comparison of biophysical and satellite predictors for wheat yield forecasting in Ukraine","volume":"40","author":"Kolotii","year":"2015","journal-title":"Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.\u2014ISPRS Arch."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1080\/22797254.2018.1454265","article-title":"Crop inventory at regional scale in Ukraine: Developing in season and end of season crop maps with multi-temporal optical and SAR satellite imagery","volume":"51","author":"Kussul","year":"2018","journal-title":"Eur. J. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Kussul, N., Shelestov, A., Lavreniuk, M., Butko, I., and Skakun, S. (2016, January 10\u201315). Deep learning approach for large scale land cover mapping based on remote sensing data fusion. Proceedings of the 2016 IEEE International Geoscience and Remote Sensing Symposium (IGARSS), Beijing, China.","DOI":"10.1109\/IGARSS.2016.7729043"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"2269","DOI":"10.1109\/TGRS.2012.2209656","article-title":"Multiple-Spectral-Band CRFs for Denoising Junk Bands of Hyperspectral Imagery","volume":"51","author":"Zhong","year":"2013","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Kumar, P., Rani, M., Chandra Pandey, P., Sajjad, H., and Chaudhary, B. (2019). Future Challenges and Perspective of Remote Sensing Technology. Applications and Challenges of Geospatial Technology, Springer.","DOI":"10.1007\/978-3-319-99882-4"},{"key":"ref_10","unstructured":"(2021, October 07). First Applications from Sentinel-2A. Available online: http:\/\/www.esa.int\/Our_Activities\/Observing_the_Earth\/Copernicus\/Sentinel-2\/First_applications_from_Sentinel-2A."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2500","DOI":"10.1109\/JSTARS.2016.2560141","article-title":"Parcel-Based Crop Classification in Ukraine Using Landsat-8 Data and Sentinel-1A Data","volume":"9","author":"Kussul","year":"2016","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1109\/MGRS.2013.2244672","article-title":"Hyperspectral Remote Sensing Data Analysis and Future Challenges","volume":"1","author":"Plaza","year":"2013","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2207","DOI":"10.1109\/JPROC.2016.2598228","article-title":"Big Data for Remote Sensing: Challenges and Opportunities","volume":"104","author":"Chi","year":"2016","journal-title":"Proc. IEEE"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Manolakis, D.G., Lockwood, R.B., and Cooley, T.W. (2016). Hyperspectral Imaging Remote Sensing: Physics, Sensors, and Algorithms, Cambridge University Press.","DOI":"10.1017\/CBO9781316017876"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"988","DOI":"10.1016\/j.actaastro.2008.12.006","article-title":"Image compression systems on board satellites","volume":"64","author":"Yu","year":"2009","journal-title":"Acta Astronaut."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Prasad, S., Bruce, L., and Chanussot, J. (2011). Hyperspectral Data Compression Tradeoff. Optical Remote Sensing in Advances in Signal Processing and Exploitation Techniques, Springer.","DOI":"10.1007\/978-3-642-14212-3"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"8","DOI":"10.1109\/MGRS.2014.2352465","article-title":"A Tutorial on Image Compression for Optical Space Imaging Systems","volume":"2","author":"Blanes","year":"2014","journal-title":"IEEE Geosci. Remote Sens. Mag."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1117\/1.JRS.8.083571","article-title":"Lossy compression of hyperspectral images based on noise parameters estimation and variance stabilizing transform","volume":"8","author":"Zemliachenko","year":"2014","journal-title":"J. Appl. Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Chow, K., Tzamarias, D.E.O., Blanes, I., and Serra-Sagrist\u00e0, J. (2019). Using Predictive and Differential Methods with K2-Raster Compact Data Structure for Hyperspectral Image Lossless Compression. Remote Sens., 11.","DOI":"10.3390\/rs11212461"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Radosavljevic, M., Brkljac, B., Lugonja, P., Crnojevic, V., Trpovski, \u017d., Xiong, Z., and Vukobratovic, D. (2020). Lossy Compression of Multispectral Satellite Images with Application to Crop Thematic Mapping: A HEVC Comparative Study. Remote Sens., 12.","DOI":"10.3390\/rs12101590"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Blanes, I., Kiely, A., Hern\u00e1ndez-Cabronero, M., and Serra-Sagrist\u00e0, J. (2019). Performance Impact of Parameter Tuning on the CCSDS-123.0-B-2 Low-Complexity Lossless and Near-Lossless Multispectral and Hyperspectral Image Compression Standard. Remote Sens., 11.","DOI":"10.3390\/rs11111390"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2547","DOI":"10.1109\/36.964993","article-title":"Near-lossless compression of 3-D optical data","volume":"39","author":"Aiazzi","year":"2001","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"850637","DOI":"10.1155\/2012\/850637","article-title":"Spectral Distortion in Lossy Compression of Hyperspectral Data","volume":"2012","author":"Aiazzi","year":"2012","journal-title":"J. Electr. Comput. Eng."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1109\/JSTARS.2011.2173906","article-title":"Performance evaluation of the H.264\/AVC video coding standard for lossy hyperspectral image compression","volume":"5","author":"Santos","year":"2012","journal-title":"IEEE J. Sel. Top. Appl. Earth Observ. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1535","DOI":"10.1615\/TelecomRadEng.v77.i17.40","article-title":"Smart Lossy Compression of Images Based on Distortion Prediction","volume":"77","author":"Krivenko","year":"2018","journal-title":"Telecommun. Radio Eng."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Vasilyeva, I., Li, F., Abramov, S., Lukin, V.V., Vozel, B., and Chehdi, K. (2021, January 12). Lossy compression of three-channel remote sensing images with controllable quality. Proceedings of the SPIE 11862, Image and Signal Processing for Remote Sensing XXVII, Madrid, Spain. Online Only.","DOI":"10.1117\/12.2599902"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1408","DOI":"10.1109\/TGRS.2007.894565","article-title":"Transform Coding Techniques for Lossy Hyperspectral Data Compression","volume":"45","author":"Penna","year":"2007","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Manolakis, D., Lockwood, R., and Cooley, T. (2008, January 7\u201311). On the Spectral Correlation Structure of Hyperspectral Imaging Data. Proceedings of the IGARSS 2008\u20142008 IEEE International Geoscience and Remote Sensing Symposium, Boston, MA, USA.","DOI":"10.1109\/IGARSS.2008.4779059"},{"key":"ref_29","first-page":"744","article-title":"The effects on image classification using image compression technique. Amsterdam","volume":"33","author":"Lam","year":"2000","journal-title":"Int. Arch. Photogramm. Remote Sens."},{"key":"ref_30","unstructured":"Meurs, M.J., and Rudzics, F. (2019). Compression improves image classification accuracy. Advances in Artificial Intelligence. Canadian AI 2019. Lecture Notes in Computer Science, Springer."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"4577","DOI":"10.1109\/TGRS.2019.2891679","article-title":"Effects of Compression on Remote Sensing Image Classification Based on Fractal Analysis","volume":"57","author":"Chen","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"5651","DOI":"10.1109\/TGRS.2019.2901396","article-title":"Improved Statistically Based Retrievals via Spatial-Spectral Data Compression for IASI Data","volume":"57","author":"Laparra","year":"2019","journal-title":"IEEE Trans. Geosci. Remote Sens."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1109\/IGARSS.2000.861642","article-title":"Introducing supervised classification into spectral VQ for multi-channel image compression","volume":"Volume 2","author":"Perra","year":"2000","journal-title":"IGARSS 2000. IEEE 2000 International Geoscience and Remote Sensing Symposium. Taking the Pulse of the Planet: The Role of Remote Sensing in Managing the Environment. Proceedings (Cat. No.00CH37120)"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2796","DOI":"10.1080\/01431161.2012.750772","article-title":"Impact of lossy compression on mapping crop areas from remote sensing","volume":"34","author":"Zabala","year":"2013","journal-title":"Int. J. Remote Sens."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Zabala, A., Pons, X., Diaz-Delgado, R., Garcia, F., Auli-Llinas, F., and Serra-Sagrista, J. (August, January 31). Effects of JPEG and JPEG2000 Lossy Compression on Remote Sensing Image Classification for Mapping Crops and Forest Areas. Proceedings of the 2006 IEEE International Symposium on Geoscience and Remote Sensing, Denver, CO, USA.","DOI":"10.1109\/IGARSS.2006.203"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Lukin, V., Vasilyeva, I., Krivenko, S., Li, F., Abramov, S., Rubel, O., Vozel, B., Chehdi, K., and Egiazarian, K. (2020). Lossy Compression of Multichannel Remote Sensing Images with Quality Control. Remote Sens., 12.","DOI":"10.3390\/rs12223840"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Taubman, D., and Marcellin, M. (2002). JPEG2000 Image Compression Fundamentals, Standards and Practice, Springer.","DOI":"10.1007\/978-1-4615-0799-4"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1109\/TMM.2008.917357","article-title":"Joined spectral trees for scalable SPIHT-based multispectral image compression","volume":"10","author":"Khelifi","year":"2008","journal-title":"IEEE Trans. Multimed."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Balasubramanian, R., and Ramakrishnan, S.S. Wavelet application in compression of a remote sensed image. Proceedings of the 2013 the International Conference on Remote Sensing, Environment and Transportation Engineering (RSETE 2013), Nanjing, China.","DOI":"10.2991\/rsete.2013.160"},{"key":"ref_40","first-page":"492","article-title":"Discrete Atomic Compression of Digital Images: A Way to Reduce Memory Expenses","volume":"Volume 113","author":"Nechyporuk","year":"2020","journal-title":"Integrated Computer Technologies in Mechanical Engineering. Advances in Intelligent Systems and Computing"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Makarichev, V.O., Lukin, V.V., Brysina, I.V., Vozel, B., and Chehdi, C. (2020, January 20). Atomic wavelets in lossy and near-lossless image compression. Proceedings of the SPIE 11533, Image and Signal Processing for Remote Sensing XXVI, Edinburgh, UK. Online Only.","DOI":"10.1117\/12.2573970"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Maniadaki, M., Papathanasopoulos, A., Mitrou, L., and Maria, E.-A. (2021). Reconciling Remote Sensing Technologies with Personal Data and Privacy Protection in the European Union: Recent Developments in Greek Legislation and Application Perspectives in Environmental Law. Laws, 10.","DOI":"10.3390\/laws10020033"},{"key":"ref_43","unstructured":"Schoenmaker, A. (2021, October 07). Community Remote Sensing Legal Issues. Available online: https:\/\/swfound.org\/media\/62081\/schoenmaker_paper_community_remote_sensing_legal_issues_final.pdf."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/s13319-017-0148-5","article-title":"A Survey of Image Encryption Algorithms","volume":"8","author":"Kumari","year":"2017","journal-title":"3D Res."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1016\/j.optlastec.2013.05.023","article-title":"A review of optical image encryption technique","volume":"57","author":"Liu","year":"2014","journal-title":"Opt. Laser Technol."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Ramakrishnan, S. (2018). Cryptographic image scrambling techniques. Cryptographic and Information Security Approaches for Images and Videos, CRC Press.","DOI":"10.1201\/9780429435461"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Makarichev, V., Lukin, V., and Brysina, I. (2020, January 14\u201318). Discrete Atomic Compression with Different Structures of Discrete Atomic Transform: Efficiency Comparison and Perspectives of Application to Digital Images Privacy Protection. Proceedings of the 2020 IEEE 11th International Conference on Dependable Systems, Services and Technologies (DESSERT), Kyiv, Ukraine.","DOI":"10.1109\/DESSERT50317.2020.9125073"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Lukin, V., Ponomarenko, N., Egiazarian, K., and Astola, J. (2015). Analysis of HVS-Metrics\u2019 Properties Using Color Image Database TID 2013. Proc. ACIVS, 613\u2013624. Available online: https:\/\/www.semanticscholar.org\/paper\/Analysis-of-HVS-Metrics\u2019-Properties-Using-Color-Ponomarenko-Lukin\/0ef7f0524a7f97af609a865e7afb102ccdf5e8e1.","DOI":"10.1007\/978-3-319-25903-1_53"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1016\/j.jvcir.2011.01.005","article-title":"Perceptual visual quality metrics: A survey","volume":"22","author":"Lin","year":"2011","journal-title":"J. Vis. Commun. Image Represent."},{"key":"ref_50","unstructured":"Ponomarenko, N., Silvestri, F., Egiazarian, K., Carli, M., Astola, J., and Lukin, V. (2007, January 25\u201326). On between-coefficient contrast masking of DCT basis functions. Proceedings of the CD-ROM Proceedings of VPQM, Scottsdale, AZ, USA."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Congalton, R.G., and Green, K. (1999). Assessing the Accuracy of Remotely Sensed Data: Principles and Practices, CRC Press.","DOI":"10.1201\/9781420048568"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"6400","DOI":"10.1016\/j.eswa.2013.05.061","article-title":"Analysis of classification accuracy for pre-filtered multichannel remote sensing data","volume":"40","author":"Lukin","year":"2013","journal-title":"J. Expert Syst. Appl."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1016\/j.mcm.2011.10.063","article-title":"Automatic remotely sensed image classification in a grid environment based on the maximum likelihood method","volume":"58","author":"Sun","year":"2013","journal-title":"Math. Comput. Model."},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Sisodia, P.S., Tiwari, V., and Kumar, A. (2014, January 9\u201311). Analysis of Supervised Maximum Likelihood Classification for remote sensing image. Proceedings of the International Conference on Recent Advances and Innovations in Engineering (ICRAIE-2014), Jaipur, India.","DOI":"10.1109\/ICRAIE.2014.6909319"},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Proskura, G., Vasilyeva, I., Fangfang, L., and Lukin, V. (2020, January 15\u201316). Classification of Compressed Multichannel Images and Its Improvement. Proceedings of the 2020 30th International Conference Radioelektronika, Bratislava, Slovakia.","DOI":"10.1109\/RADIOELEKTRONIKA49387.2020.9092371"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1641","DOI":"10.1109\/83.730376","article-title":"Lossy compression of noisy images","volume":"7","author":"Mersereau","year":"1998","journal-title":"IEEE Trans. Image Process."},{"key":"ref_57","first-page":"42","article-title":"On the Applications of the Special Class of Atomic Functions: Practical Aspects and Perspectives","volume":"Volume 188","author":"Nechyporuk","year":"2021","journal-title":"Integrated Computer Technologies in Mechanical Engineering\u20142020. ICTM 2020. Lecture Notes in Networks and Systems"},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Sayood, K. (2017). Introduction to Data Compression, Morgan Kaufman. [4th ed.].","DOI":"10.1016\/B978-0-12-809474-7.00019-7"},{"key":"ref_59","unstructured":"Bryant, R.E., and O\u2019Hallaron, D.R. (2010). Computer Systems: A Programmer\u2019s Perspective, Pearson. [2nd ed.]."},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"44","DOI":"10.32620\/reks.2020.1.05","article-title":"On estimates of coefficients of generalized atomic wavelets expansions and their application to data processing","volume":"93","author":"Makarichev","year":"2020","journal-title":"Radioelectron. Comput. Syst."},{"key":"ref_61","doi-asserted-by":"crossref","unstructured":"Welstead, S. (1999). Fractal and Wavelet Image Compression Techniques, SPIE Publications.","DOI":"10.1117\/3.353798"},{"key":"ref_62","unstructured":"(2021, October 07). WebP, Compression Techniques. Available online: https:\/\/developers.google.com\/speed\/webp\/docs\/compression."},{"key":"ref_63","doi-asserted-by":"crossref","unstructured":"Kotz, S., Balakrishnan, N., Read, C., Vidakovic, B., and Johnson, N.L. (2005). Encyclopedia of Statistical Sciences, Wiley-Interscience. [2nd ed.].","DOI":"10.1002\/0471667196"},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Olive, D.J. (2017). Linear Regression, Springer.","DOI":"10.1007\/978-3-319-55252-1"},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Makarichev, V.O., Lukin, V.V., Brysina, I.V., Vozel, B., and Chehdi, C. (2021, January 12). Discrete atomic compression of satellite images: A comprehensive efficiency research. Proceedings of the SPIE 11862, Image and Signal Processing for Remote Sensing XXVII, Madrid, Spain. 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