{"id":102611,"date":"2020-12-06T16:44:39","date_gmt":"2020-12-06T16:44:39","guid":{"rendered":"http:\/\/ahay.org\/blog\/?p=102611"},"modified":"2020-12-06T16:44:39","modified_gmt":"2020-12-06T16:44:39","slug":"seismic-signal-enhancement-based-on-the-lowrank-methods","status":"publish","type":"post","link":"https:\/\/ahay.org\/blog\/2020\/12\/06\/seismic-signal-enhancement-based-on-the-lowrank-methods\/","title":{"rendered":"Seismic signal enhancement based on the lowrank methods"},"content":{"rendered":"<p>A new paper is added to the <a href=\"\/wiki\/Reproducible_Documents\">collection of reproducible documents<\/a>: <a href=\"\/RSF\/book\/zju\/odrr3d\/paper_html\/\">Seismic signal enhancement based on the lowrank methods<\/a><\/p>\n<p><img decoding=\"async\" src=\"\/RSF\/book\/zju\/odrr3d\/Fig\/r3d-z.png\" alt=\"\" title=\"\"><br \/>\n<img decoding=\"async\" src=\"\/RSF\/book\/zju\/odrr3d\/Fig\/r3d-olr-z0.png\" alt=\"\" title=\"\"><\/p>\n<blockquote><p>Based on the fact that the Hankel matrix constructed by noise-free seismic data is lowrank (LR), LR approximation (or rank-reduction) methods have been widely used for removing noise from seismic data. Due to the linear-event assumption of the traditional LR approximation method, it is difficult to define a rank that optimally separates the data subspace into signal and noise subspaces. For preserving the most useful signal energy, a relatively large rank threshold is often chosen, which inevitably leaves residual noise. To reduce the energy of residual noise, we propose an optimally damped rank-reduction method. The optimal damping is applied via two steps. In the first step, a set of optimal damping weights is derived. In the second step, we derive an optimal singular-value damping operator. We review several traditional lowrank methods and compare their performance with the new one. We also compare these lowrank methods with two sparsity-promoting transform methods. Examples demonstrate that the proposed optimally damped rank-reduction method could get significantly cleaner denoised images compared with the state-of-the-art methods.<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>A new paper is added to the collection of reproducible documents: Seismic signal enhancement based on the lowrank methods Based on the fact that the Hankel matrix constructed by noise-free seismic data is lowrank (LR), LR approximation (or rank-reduction) methods have been widely used for removing noise from seismic data. Due to the linear-event assumption [&hellip;]<\/p>\n","protected":false},"author":15,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_import_markdown_pro_load_document_selector":0,"_import_markdown_pro_submit_text_textarea":"","activitypub_content_warning":"","activitypub_content_visibility":"","activitypub_max_image_attachments":4,"activitypub_interaction_policy_quote":"anyone","activitypub_status":"","footnotes":""},"categories":[5],"tags":[],"class_list":["post-102611","post","type-post","status-publish","format-standard","hentry","category-documentation"],"_links":{"self":[{"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/posts\/102611","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/users\/15"}],"replies":[{"embeddable":true,"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/comments?post=102611"}],"version-history":[{"count":1,"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/posts\/102611\/revisions"}],"predecessor-version":[{"id":102612,"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/posts\/102611\/revisions\/102612"}],"wp:attachment":[{"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/media?parent=102611"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/categories?post=102611"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ahay.org\/blog\/wp-json\/wp\/v2\/tags?post=102611"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}