{"id":1267,"date":"2025-07-15T15:31:06","date_gmt":"2025-07-15T15:31:06","guid":{"rendered":"https:\/\/smartdata.ece.ufl.edu\/?p=1267"},"modified":"2025-06-09T15:39:09","modified_gmt":"2025-06-09T15:39:09","slug":"sparse-wavenumber-recovery-in-anisotropic-composites-codeocean-repository-summary","status":"publish","type":"post","link":"https:\/\/smartdata.ece.ufl.edu\/index.php\/2025\/07\/15\/sparse-wavenumber-recovery-in-anisotropic-composites-codeocean-repository-summary\/","title":{"rendered":"Sparse Wavenumber Recovery in Anisotropic Composites Repository"},"content":{"rendered":"\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-a89b3969 wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button has-custom-width wp-block-button__width-50\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/codeocean.com\/capsule\/2176514\/tree\/v1\">Get the Code (Code Ocean)<\/a><\/div>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Summary<\/h2>\n\n\n\n<p>Guided wave imaging is a cornerstone technique in structural health monitoring (SHM), especially for <strong>composite materials<\/strong>. But composites are <strong>anisotropic<\/strong>\u2014meaning wave speeds and behaviors vary with direction\u2014which makes interpreting wave propagation challenging.<\/p>\n\n\n\n<p>This <a class=\"\" href=\"https:\/\/codeocean.com\/capsule\/2176514\/tree\/v1\">CodeOcean capsule<\/a> presents the algorithm and tools for <strong>Sparse Wavenumber Recovery (SWR)<\/strong> developed by <strong>Soroosh Sabeti<\/strong>, which leverage compressed sensing and sparse signal processing to efficiently extract <strong>anisotropic wavenumber content<\/strong> from limited measurements.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83c\udfaf Why This Matters<\/h3>\n\n\n\n<p>Conventional Fourier-based methods for wavefield analysis (e.g., 2D FFT) require <strong>dense spatial sampling<\/strong>, which is impractical in many real-world settings. SWR addresses this limitation by enabling:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Accurate <strong>recovery of direction-dependent wavenumbers<\/strong> (i.e., dispersion),<\/li>\n\n\n\n<li>From <strong>sparse or non-uniform measurements<\/strong>,<\/li>\n\n\n\n<li>While remaining robust to <strong>anisotropic material behaviors<\/strong>, such as in carbon fiber composites.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udcd0 Core Technical Idea<\/h3>\n\n\n\n<p>Given a spatial wavefield snapshot <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/smartdata.ece.ufl.edu\/wp-content\/ql-cache\/quicklatex.com-8516452747e93c1471f4460fe20b5f2a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#117;&#40;&#120;&#44;&#32;&#121;&#44;&#32;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"64\" style=\"vertical-align: -5px;\"\/>, the goal is to identify the <strong>dominant wavenumber vectors<\/strong> <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/smartdata.ece.ufl.edu\/wp-content\/ql-cache\/quicklatex.com-05ba5848f5768a8afb67da404f2a77f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#118;&#101;&#99;&#123;&#107;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"11\" style=\"vertical-align: 0px;\"\/> that represent wave propagation at different angles <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/smartdata.ece.ufl.edu\/wp-content\/ql-cache\/quicklatex.com-7b2034939b850e3311120fca462ab64e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#104;&#101;&#116;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"\/>.<\/p>\n\n\n\n<p>Traditional methods use the 2D spatial Fourier transform: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/smartdata.ece.ufl.edu\/wp-content\/ql-cache\/quicklatex.com-1616f60d6bf392838f713243a01176a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#104;&#97;&#116;&#123;&#117;&#125;&#40;&#107;&#95;&#120;&#44;&#32;&#107;&#95;&#121;&#41;&#32;&#61;&#32;&#92;&#109;&#97;&#116;&#104;&#99;&#97;&#108;&#123;&#70;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"106\" style=\"vertical-align: -6px;\"\/><\/p>\n\n\n\n<p>but require Nyquist-level sampling. Instead, Sparse Wavenumber Recovery solves: <p class=\"ql-center-displayed-equation\" style=\"line-height: 24px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/smartdata.ece.ufl.edu\/wp-content\/ql-cache\/quicklatex.com-1924126e761e366aa300f5b7b4c9e5f5_l3.png\" height=\"24\" width=\"254\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#32;&#92;&#109;&#105;&#110;&#95;&#123;&#92;&#97;&#108;&#112;&#104;&#97;&#125;&#32;&#92;&#124;&#32;&#92;&#97;&#108;&#112;&#104;&#97;&#32;&#92;&#124;&#95;&#49;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#117;&#98;&#106;&#101;&#99;&#116;&#32;&#116;&#111;&#125;&#32;&#92;&#113;&#117;&#97;&#100;&#32;&#117;&#32;&#61;&#32;&#92;&#80;&#104;&#105;&#32;&#92;&#80;&#115;&#105;&#32;&#92;&#97;&#108;&#112;&#104;&#97;&#32;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/smartdata.ece.ufl.edu\/wp-content\/ql-cache\/quicklatex.com-e817933126862db10ae510d35359568e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#117;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"\/>: measured spatial wavefield vector (possibly under-sampled),<\/li>\n\n\n\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/smartdata.ece.ufl.edu\/wp-content\/ql-cache\/quicklatex.com-21f36758b04341c7980aa18b13ced720_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#80;&#104;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/>: sampling matrix,<\/li>\n\n\n\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/smartdata.ece.ufl.edu\/wp-content\/ql-cache\/quicklatex.com-96d558896734bc27372c9e3216e687db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#80;&#115;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\"\/>: wavenumber dictionary (e.g., plane wave atoms at various <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/smartdata.ece.ufl.edu\/wp-content\/ql-cache\/quicklatex.com-05ba5848f5768a8afb67da404f2a77f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#118;&#101;&#99;&#123;&#107;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"11\" style=\"vertical-align: 0px;\"\/>),<\/li>\n\n\n\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/smartdata.ece.ufl.edu\/wp-content\/ql-cache\/quicklatex.com-5f44d9bbc8046069be4aa2989bff19aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#97;&#108;&#112;&#104;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"\/>: sparse representation of wavefield in the wavenumber domain.<\/li>\n<\/ul>\n\n\n\n<p>This formulation promotes <strong>sparse solutions<\/strong>\u2014capturing only the most physically meaningful wave directions and speeds.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83e\uddea What\u2019s in the Repository?<\/h3>\n\n\n\n<p>The <a class=\"\" href=\"https:\/\/codeocean.com\/capsule\/2176514\/tree\/v1\">CodeOcean capsule<\/a> includes:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2705 MATLAB scripts to implement sparse recovery using L1-norm minimization,<\/li>\n\n\n\n<li>\ud83d\udcca Visualizations of anisotropic wave propagation in composite panels,<\/li>\n\n\n\n<li>\ud83e\udde0 Comparative studies with traditional FFT and MUSIC algorithms,<\/li>\n\n\n\n<li>\ud83d\udcc2 Sample data from finite element simulations and experiments.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udd2c What Did the Paper Show?<\/h3>\n\n\n\n<p>The authors tested SWR on both <strong>simulated<\/strong> and <strong>experimental Lamb wave data<\/strong> from composite plates. Their results show:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>SWR accurately reconstructs <strong>anisotropic dispersion curves<\/strong>, even from 10\u201320% of spatial data.<\/li>\n\n\n\n<li>It outperforms MUSIC and FFT in both <strong>angular resolution<\/strong> and <strong>robustness to noise<\/strong>.<\/li>\n\n\n\n<li>The method reveals direction-dependent wave speeds and mode interactions not easily seen in conventional spectra.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udca1 Real-World Impact<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\ud83d\udee9\ufe0f Ideal for aerospace composites and curved laminate structures,<\/li>\n\n\n\n<li>\ud83d\udd0e Supports SHM systems with <strong>limited sensor counts<\/strong>,<\/li>\n\n\n\n<li>\ud83e\uddf1 Can be combined with machine learning for automated defect detection,<\/li>\n\n\n\n<li>\ud83d\udcc9 Enables better <strong>modal separation<\/strong> and <strong>phase velocity estimation<\/strong>.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83d\udcda Reference<\/h3>\n\n\n\n<p><strong>Sabeti, S., Leckey, C. A. C., De Marchi, L., &amp; Harley, J. B. (2019).<\/strong><br><em>Sparse Wavenumber Recovery and Prediction of Anisotropic Guided Waves in Composites: A Comparative Study.<\/em><br><em>IEEE Trans. on Ultrasonics, Ferroelectrics, and Frequency Control, 66(8), 1352\u20131363.<\/em><br>\ud83d\udd17 <a class=\"\" href=\"https:\/\/ieeexplore.ieee.org\/document\/8721165\">https:\/\/ieeexplore.ieee.org\/document\/8721165<\/a><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>This repository offers a practical, efficient, and research-validated toolkit for guided wave analysis in complex composite structures. Whether you&#8217;re designing SHM systems, interpreting wavefields, or experimenting with anisotropy-aware imaging, <strong>SWR gives you sharper insights with fewer sensors<\/strong>.<\/p>\n\n\n\n<p><strong>Sparse data. Rich understanding.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Guided wave imaging is a cornerstone technique in structural health monitoring (SHM), especially for composite materials. But composites are anisotropic\u2014meaning wave speeds and behaviors vary with direction\u2014which makes interpreting wave propagation challenging.<\/p>\n<p>This CodeOcean capsule presents the algorithm and tools for Sparse Wavenumber Recovery (SWR) developed by Soroosh Sabeti, which leverage compressed sensing and sparse signal processing to efficiently extract anisotropic wavenumber content from limited measurements.<\/p>\n","protected":false},"author":1,"featured_media":941,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21],"tags":[58,17,65,16,12,14,40,13,39],"class_list":["post-1267","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-code-resources","tag-anisotropy","tag-eigenmodes","tag-lamb-waves","tag-linear-algebra","tag-mechanics","tag-nondestructive-testing","tag-sparse-wavenumber-analysis","tag-structural-health-monitoring","tag-undersampling"],"_links":{"self":[{"href":"https:\/\/smartdata.ece.ufl.edu\/index.php\/wp-json\/wp\/v2\/posts\/1267","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/smartdata.ece.ufl.edu\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/smartdata.ece.ufl.edu\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/smartdata.ece.ufl.edu\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/smartdata.ece.ufl.edu\/index.php\/wp-json\/wp\/v2\/comments?post=1267"}],"version-history":[{"count":5,"href":"https:\/\/smartdata.ece.ufl.edu\/index.php\/wp-json\/wp\/v2\/posts\/1267\/revisions"}],"predecessor-version":[{"id":1269,"href":"https:\/\/smartdata.ece.ufl.edu\/index.php\/wp-json\/wp\/v2\/posts\/1267\/revisions\/1269"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/smartdata.ece.ufl.edu\/index.php\/wp-json\/wp\/v2\/media\/941"}],"wp:attachment":[{"href":"https:\/\/smartdata.ece.ufl.edu\/index.php\/wp-json\/wp\/v2\/media?parent=1267"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/smartdata.ece.ufl.edu\/index.php\/wp-json\/wp\/v2\/categories?post=1267"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/smartdata.ece.ufl.edu\/index.php\/wp-json\/wp\/v2\/tags?post=1267"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}