{"id":1216,"date":"2025-06-03T02:39:51","date_gmt":"2025-06-03T02:39:51","guid":{"rendered":"https:\/\/smartdata.ece.ufl.edu\/?p=1216"},"modified":"2026-04-07T13:09:38","modified_gmt":"2026-04-07T13:09:38","slug":"temporal-sparse-wavenumber-analysis-repository","status":"publish","type":"post","link":"https:\/\/smartdata.ece.ufl.edu\/index.php\/2025\/06\/03\/temporal-sparse-wavenumber-analysis-repository\/","title":{"rendered":"Temporal Sparse Wavenumber Analysis Repository"},"content":{"rendered":"\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-3e41869c 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 has-text-align-center wp-element-button\" href=\"https:\/\/codeocean.com\/capsule\/7876443\/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 class=\"wp-block-paragraph\"><strong>Temporal Sparse Wavenumber Analysis (TSWA)<\/strong> is a novel technique that reconstructs high-resolution spatiotemporal wavefields using <strong>fewer temporal samples<\/strong> than traditional methods typically require. Developed by <strong>Soroosh Sabeti<\/strong> and <strong>Dr. Joel B. Harley<\/strong>, TSWA makes it possible to retrieve accurate guided wave information from temporally undersampled data, which is crucial in applications where <strong>high-speed sensing<\/strong>, <strong>data storage<\/strong>, or <strong>power consumption<\/strong> are limiting factors.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This <a class=\"\" href=\"https:\/\/codeocean.com\/capsule\/7876443\/tree\/v1\">CodeOcean capsule<\/a> contains a full implementation of TSWA, as described in:<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p class=\"wp-block-paragraph\"><strong>Sabeti, S., &amp; Harley, J. B. (2017).<\/strong> <em>Guided wave retrieval from temporally undersampled data<\/em>. 2017 IEEE International Ultrasonics Symposium (IUS), 1\u20134. <a href=\"https:\/\/doi.org\/10.1109\/ULTSYM.2017.8091996\" data-type=\"link\" data-id=\"https:\/\/doi.org\/10.1109\/ULTSYM.2017.8091996\">https:\/\/doi.org\/10.1109\/ULTSYM.2017.8091996<\/a><\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">? Why TSWA?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Conventional methods of wavefield reconstruction require <strong>Nyquist-rate temporal sampling<\/strong>, leading to high data acquisition and storage burdens. In practice, this restricts sensing systems on <strong>resource-constrained platforms<\/strong> like embedded SHM systems or UAVs. TSWA overcomes this by using <strong>compressive sensing<\/strong> to reconstruct wavefields from <strong>fewer temporal samples<\/strong>, enabling <strong>efficient, high-resolution guided wave analysis<\/strong> without compromising signal integrity.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">? How It Works<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The core idea of TSWA is to exploit the <strong>sparsity<\/strong> of a wavefield in the <strong>wavenumber domain<\/strong> and recover full-resolution temporal signals from sub-sampled data using sparse optimization.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let:<\/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-0ab7ba7a9e086ff8eab52fe1e384ad13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#117;&#40;&#120;&#44;&#32;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"47\" style=\"vertical-align: -5px;\"\/> be the recorded wavefield at spatial location <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/smartdata.ece.ufl.edu\/wp-content\/ql-cache\/quicklatex.com-7e5fbfa0bbbd9f3051cd156a0f1b5e31_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#120;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"\/> and time <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/smartdata.ece.ufl.edu\/wp-content\/ql-cache\/quicklatex.com-fd9cb27edab3f0a8a249bc80cc9c6ee2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#116;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"\/>.<\/li>\n\n\n\n<li>The wavefield is modeled as a superposition of a <strong>sparse set of propagating plane waves<\/strong>.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">TSWA assumes that the wavefield can be expressed as:  <p class=\"ql-center-displayed-equation\" style=\"line-height: 52px;\"><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-a3f8f32d9a71e6e82fb636b5fbe5eb55_l3.png\" height=\"52\" width=\"199\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#91;&#32;&#117;&#40;&#120;&#44;&#32;&#116;&#41;&#32;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#92;&#115;&#117;&#109;&#95;&#123;&#110;&#61;&#49;&#125;&#94;&#78;&#32;&#97;&#95;&#110;&#32;&#101;&#94;&#123;&#106;&#40;&#107;&#95;&#110;&#32;&#120;&#32;&#45;&#32;&#92;&#111;&#109;&#101;&#103;&#97;&#95;&#110;&#32;&#116;&#41;&#125;&#32;&#92;&#93;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">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-5a64427cd35de68f79a3fc97a1355e4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#97;&#95;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"17\" style=\"vertical-align: -3px;\"\/>\u200b are the complex amplitudes,<\/li>\n\n\n\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/smartdata.ece.ufl.edu\/wp-content\/ql-cache\/quicklatex.com-0179eb3e04d0d3e304e4cd04a9ed34dc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#107;&#95;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"17\" style=\"vertical-align: -3px;\"\/>\u200b are candidate spatial frequencies (wavenumbers),<\/li>\n\n\n\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/smartdata.ece.ufl.edu\/wp-content\/ql-cache\/quicklatex.com-af00a3620b24abafc0ca8201b72cc272_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#111;&#109;&#101;&#103;&#97;&#95;&#110;\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"19\" style=\"vertical-align: -3px;\"\/>\u200b are the associated angular frequencies.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">If we denote the temporally undersampled measurement vector as <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/smartdata.ece.ufl.edu\/wp-content\/ql-cache\/quicklatex.com-3818773d55ab7e8be9afbd41dc6c63eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"11\" style=\"vertical-align: -4px;\"\/>, the reconstruction problem becomes: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/smartdata.ece.ufl.edu\/wp-content\/ql-cache\/quicklatex.com-5c4ae2793387328b1c81b42dd51d1142_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#109;&#105;&#110;&#95;&#123;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#97;&#125;&#125;&#32;&#92;&#124;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#121;&#125;&#32;&#45;&#32;&#92;&#80;&#104;&#105;&#32;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#97;&#125;&#32;&#92;&#124;&#95;&#50;&#94;&#50;&#32;&#43;&#32;&#92;&#108;&#97;&#109;&#98;&#100;&#97;&#32;&#92;&#124;&#92;&#109;&#97;&#116;&#104;&#98;&#102;&#123;&#97;&#125;&#92;&#124;&#95;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"188\" style=\"vertical-align: -5px;\"\/><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">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-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;\"\/> is the <strong>dictionary matrix<\/strong> of plane waves evaluated at known spatial and undersampled temporal locations,<\/li>\n\n\n\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/smartdata.ece.ufl.edu\/wp-content\/ql-cache\/quicklatex.com-8c37d2f1acb1d49f3e5e655797880475_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#108;&#97;&#109;&#98;&#100;&#97;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"10\" style=\"vertical-align: 0px;\"\/> is a regularization parameter enforcing sparsity.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">This sparse recovery allows reconstruction of the full spatiotemporal wavefield, even from temporally incomplete data.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2699\ufe0f What\u2019s in This Capsule?<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u2705 Full MATLAB implementation of the TSWA algorithm<\/li>\n\n\n\n<li>? Synthetic and experimental datasets for demonstration<\/li>\n\n\n\n<li>? Tools to visualize reconstructed wavefields and compare with ground truth<\/li>\n\n\n\n<li>? Documentation and usage examples for reproducibility<\/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\">? Key Benefits<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>? <strong>Reduced temporal sampling<\/strong> \u2014 up to 50% fewer time points with minimal loss in accuracy<\/li>\n\n\n\n<li>? <strong>High-resolution wavefield reconstruction<\/strong> \u2014 sharp, artifact-free spatiotemporal profiles<\/li>\n\n\n\n<li>\u26a1 <strong>Efficiency<\/strong> \u2014 lowers data acquisition and processing demands<\/li>\n\n\n\n<li>? <strong>Adaptable<\/strong> \u2014 compatible with structural health monitoring, NDE, and ultrasonics<\/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\">? Reference<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Sabeti, S., &amp; Harley, J. B. (2017). <em>Guided wave retrieval from temporally undersampled data<\/em>. In <em>2017 IEEE International Ultrasonics Symposium (IUS)<\/em> (pp. 1\u20134). IEEE. <a href=\"https:\/\/doi.org\/10.1109\/ULTSYM.2017.8091996\" data-type=\"link\" data-id=\"https:\/\/doi.org\/10.1109\/ULTSYM.2017.8091996\">https:\/\/doi.org\/10.1109\/ULTSYM.2017.8091996<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Temporal Sparse Wavenumber Analysis (TSWA) is a novel technique that reconstructs high-resolution spatiotemporal wavefields using fewer temporal samples than traditional methods typically require. Developed by Soroosh Sabeti and Dr. Joel B. Harley, TSWA makes it possible to retrieve accurate guided wave information from temporally undersampled data, which is crucial in applications where high-speed sensing, data storage, or power consumption are limiting factors.<\/p>\n","protected":false},"author":1,"featured_media":843,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[21],"tags":[17,16,14,40,13,39],"class_list":["post-1216","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-code-resources","tag-eigenmodes","tag-linear-algebra","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\/1216","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=1216"}],"version-history":[{"count":3,"href":"https:\/\/smartdata.ece.ufl.edu\/index.php\/wp-json\/wp\/v2\/posts\/1216\/revisions"}],"predecessor-version":[{"id":1220,"href":"https:\/\/smartdata.ece.ufl.edu\/index.php\/wp-json\/wp\/v2\/posts\/1216\/revisions\/1220"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/smartdata.ece.ufl.edu\/index.php\/wp-json\/wp\/v2\/media\/843"}],"wp:attachment":[{"href":"https:\/\/smartdata.ece.ufl.edu\/index.php\/wp-json\/wp\/v2\/media?parent=1216"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/smartdata.ece.ufl.edu\/index.php\/wp-json\/wp\/v2\/categories?post=1216"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/smartdata.ece.ufl.edu\/index.php\/wp-json\/wp\/v2\/tags?post=1216"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}