[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125681-en":3,"doc-seo-125681-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},125681,8796095360427,"Lucas Martin","https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d",8,"Research & Report","Interferometric SAR Coherence Magnitude Estimation by Machine Learning - Research Focus","Wide area InSAR services require coherence magnitude to be estimated with high accuracy and low computation. A missing method simultaneously achieves precision and efficiency, motivating improved empirical Bayesian coherence magnitude estimation in terms of accuracy and computational cost. The paper proposes interferometric coherence magnitude estimation by machine learning as a non-parametric, automated statistical inference, while addressing the difficulty of covering infinite input domains. Results report bias, standard deviation, and RMSE showing ML gains for small samples and low coherence. The approach is suited for operational InSAR because evaluation is extremely fast, without iteration, numeric integration, or bootstrapping.","This article has been accepted for publication in IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing. This is the author's version which has not been fully  \ncontent may change prior to final publication. Citation information: DOI 10. 1109/JSTARS.2023.3257047  \nIEEE JOURNAL OF SELECTED TOPICS IN APPLIED EARTH OBSERVATIONS AND REMOTE SENSING 1  \nInterferometric SAR Coherence Magnitude Estimation by Machine Learning  \nNico Adam   \nAbstract—Current interferometric wide area ground motion services require the estimation of the coherence magnitude as accurately and computationally effectively as possible. However, a precise and at the same time computationally efficient method is missing. Therefore, the objective of this article is to improve the empirical Bayesian coherence magnitude estimation in terms of accuracy and computational cost. Precisely, this article proposes the interferometric coherence magnitude estimation by Machine Learning (ML).  \nIt results in a non-parametric and automated statistical inference. However, applying ML in this estimation context is not straightforward. The number and the domain of possible input processes is infinite and it is not possible to train all possible input signals. It is shown that the expected channel amplitudesand the expected interferometric phase cause redundancies in the input signals allowing to solve this issue. Similar to the empirical Bayesian methods, a single parameter for the maximum underlaying coherence is used to model the prior. However, no prior or any shape of prior probability is easy to implement within the ML framework.  \nThe article reports on the bias, the standard deviation and the root mean square error (RMSE) of the developed estimators. It was found that ML estimators improve the coherence estimation RMSE from small samples (2 ≤ N \u003C 30) and for small underlaying coherence compared to the conventional and empirical Bayes estimators. For three interferometric samples (N = 3) and a zero coherence magnitude, the bias related to the sample estimator improves from 0.53 to 0.39 by 27.8%. Assuming the maximum underlaying coherence is 0.6, the bias is reduced by 33.0% to 0.36 for the less strict and by 45.5% to 0.29 for the strict prior.  \nThe developed ML coherence magnitude estimators are suitable and recommended for operational InSAR systems. For the estimation, the ML model is extremely fast evaluated because no iteration, numeric integration or Bootstrapping is needed.  \nIndex Terms—Coherence magnitude, degree of coherence, distributed scatterer in SqueeSAR or CESAR or phase linking, Gradient Boosted Trees, interferometric SAR (InSAR), Supervised Machine Learning  \nI. INTRODUCTION  \nIN recent years, SAR interferometry (InSAR) has developed  \nrapidly and now allows continuous monitoring of subtle deformations of the Earth’s surface with millimeter accuracy [1], [2], [3] . There is an increasing number of wide area operational services such as the European Ground Motion Service (EGMS) [4], [5], [6] and the Ground Motion Service Germany [7], [8], [9] that make the deformation maps freely available and thus widely visible. For their production, the coherence magnitude is an essential estimate, since this is the crucial weighting [10] in all estimation methods based on distributed scatterers. Due to the large amount of data and the significance, there is an actual need to estimate this parameter as accurately and computationally effectively as possible. Technically, the task is to estimate the population  \nparameter coherence magnitude from a sample of size N. However, the challenges are the bias and variance of the estimate, which are large for small coherences and small sample sizes, and the high computational cost of using more precise methods.  \nThis article proposes the interferometric coherence magnitude estimation by Machine Learning (ML) . ML has made alot of progress in recent years and has already found numerous applications in r","cbCaivx2X3TwVx6x","https://ap.wps.com/l/cbCaivx2X3TwVx6x","pdf",1883884,1,11,"English","en",105,"# Abstract\n# Introduction\n## Problem setting for coherence magnitude estimation\n## Conventional and Bayesian baselines\n## Relation to statistical inference and distributed scatterers","[{\"question\":\"What problem does the paper address in InSAR coherence magnitude estimation?\",\"answer\":\"It addresses the need for estimating interferometric coherence magnitude with both high accuracy and computational efficiency, where a precise yet efficient method has been lacking.\"},{\"question\":\"How does the proposed method differ from empirical Bayesian estimation?\",\"answer\":\"The method formulates coherence magnitude estimation as machine learning-based, providing non-parametric, automated statistical inference while still using a prior modeled via a single parameter for maximum underlying coherence.\"},{\"question\":\"When do the machine learning estimators show the largest improvement?\",\"answer\":\"They improve RMSE for small sample sizes (2 ≤ N \\u003c 30) and for small underlying coherence compared with conventional and empirical Bayes estimators, with further bias reductions reported for specific cases such as N = 3 and zero coherence.\"}]","Interferometric SAR Coherence Magnitude Estimation by Machine Learning - 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