{"action":"created","issue":{"url":"https://api.github.com/repos/PyAbel/PyAbel/issues/167","repository_url":"https://api.github.com/repos/PyAbel/PyAbel","labels_url":"https://api.github.com/repos/PyAbel/PyAbel/issues/167/labels{/name}","comments_url":"https://api.github.com/repos/PyAbel/PyAbel/issues/167/comments","events_url":"https://api.github.com/repos/PyAbel/PyAbel/issues/167/events","html_url":"https://github.com/PyAbel/PyAbel/issues/167","id":149175943,"number":167,"title":"Incorporate Lin-BASEX Method into PyAbel","user":{"login":"DanHickstein","id":1107796,"avatar_url":"https://avatars.githubusercontent.com/u/1107796?v=3","gravatar_id":"","url":"https://api.github.com/users/DanHickstein","html_url":"https://github.com/DanHickstein","followers_url":"https://api.github.com/users/DanHickstein/followers","following_url":"https://api.github.com/users/DanHickstein/following{/other_user}","gists_url":"https://api.github.com/users/DanHickstein/gists{/gist_id}","starred_url":"https://api.github.com/users/DanHickstein/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DanHickstein/subscriptions","organizations_url":"https://api.github.com/users/DanHickstein/orgs","repos_url":"https://api.github.com/users/DanHickstein/repos","events_url":"https://api.github.com/users/DanHickstein/events{/privacy}","received_events_url":"https://api.github.com/users/DanHickstein/received_events","type":"User","site_admin":false},"labels":[{"url":"https://api.github.com/repos/PyAbel/PyAbel/labels/discussion","name":"discussion","color":"fef2c0"},{"url":"https://api.github.com/repos/PyAbel/PyAbel/labels/enhancement","name":"enhancement","color":"84b6eb"},{"url":"https://api.github.com/repos/PyAbel/PyAbel/labels/help%20wanted","name":"help wanted","color":"159818"}],"state":"open","locked":false,"assignee":{"login":"stggh","id":10932229,"avatar_url":"https://avatars.githubusercontent.com/u/10932229?v=3","gravatar_id":"","url":"https://api.github.com/users/stggh","html_url":"https://github.com/stggh","followers_url":"https://api.github.com/users/stggh/followers","following_url":"https://api.github.com/users/stggh/following{/other_user}","gists_url":"https://api.github.com/users/stggh/gists{/gist_id}","starred_url":"https://api.github.com/users/stggh/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/stggh/subscriptions","organizations_url":"https://api.github.com/users/stggh/orgs","repos_url":"https://api.github.com/users/stggh/repos","events_url":"https://api.github.com/users/stggh/events{/privacy}","received_events_url":"https://api.github.com/users/stggh/received_events","type":"User","site_admin":false},"milestone":{"url":"https://api.github.com/repos/PyAbel/PyAbel/milestones/4","html_url":"https://github.com/PyAbel/PyAbel/milestones/Version%200.9","labels_url":"https://api.github.com/repos/PyAbel/PyAbel/milestones/4/labels","id":1631340,"number":4,"title":"Version 0.9","description":"","creator":{"login":"DanHickstein","id":1107796,"avatar_url":"https://avatars.githubusercontent.com/u/1107796?v=3","gravatar_id":"","url":"https://api.github.com/users/DanHickstein","html_url":"https://github.com/DanHickstein","followers_url":"https://api.github.com/users/DanHickstein/followers","following_url":"https://api.github.com/users/DanHickstein/following{/other_user}","gists_url":"https://api.github.com/users/DanHickstein/gists{/gist_id}","starred_url":"https://api.github.com/users/DanHickstein/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DanHickstein/subscriptions","organizations_url":"https://api.github.com/users/DanHickstein/orgs","repos_url":"https://api.github.com/users/DanHickstein/repos","events_url":"https://api.github.com/users/DanHickstein/events{/privacy}","received_events_url":"https://api.github.com/users/DanHickstein/received_events","type":"User","site_admin":false},"open_issues":1,"closed_issues":0,"state":"open","created_at":"2016-03-08T19:02:49Z","updated_at":"2016-04-18T14:58:50Z","due_on":null,"closed_at":null},"comments":23,"created_at":"2016-04-18T14:58:50Z","updated_at":"2016-04-25T14:50:56Z","closed_at":null,"body":"Thomas Gerber of the Paul Scherrer Institut contacted us and offered to let his Lin-BASEX method be incorporated into PyAbel!\r\n\r\nThe method is already implemented in an iPython Notebook:\r\n\r\nDownload: https://www.psi.ch/sls/vuv/Station1_IntroEN/Lin_Basex0.7.zip\r\nReference: http://dx.doi.org/10.1063/1.4793404\r\nPDF: http://www.nccr-must.ch/libraries.files/Gerber-2013.pdf\r\nAmusing drawing of pig with a top hat: https://www.psi.ch/sls/vuv/pepico\r\n\r\nI just started reading about this method this morning, but it seems very interesting and quite different from out other methods. Fundamentally, it expands the projection in terms of Legendre polynomials (or other polynomials optionally?), so I think that it assumes a \"VMI-like\" image. This limits the applicability of the algorithm somewhat, but provides the huge bonus of eliminating much of the noise from a VMI image.\r\n\r\nIn contrast to the Polar Onion Peeling method (https://github.com/PyAbel/PyAbel/issues/30), which I believe fits Legendre polynomials to the entire 2D image, the Lin-Basex method appears to take 1D projections of the original image at different angles and fits the Legendre polynomials to these. This serves to reduce the numerical complexity of the problem. To some degree, I think that this also makes the approximation that the angular distribution is slowly varying with angle. Presumably, the number of projections can be decreased to provide faster transforms at the cost of making the \"slowly varying with angle\" approximation stronger."},"comment":{"url":"https://api.github.com/repos/PyAbel/PyAbel/issues/comments/214371348","html_url":"https://github.com/PyAbel/PyAbel/issues/167#issuecomment-214371348","issue_url":"https://api.github.com/repos/PyAbel/PyAbel/issues/167","id":214371348,"user":{"login":"DanHickstein","id":1107796,"avatar_url":"https://avatars.githubusercontent.com/u/1107796?v=3","gravatar_id":"","url":"https://api.github.com/users/DanHickstein","html_url":"https://github.com/DanHickstein","followers_url":"https://api.github.com/users/DanHickstein/followers","following_url":"https://api.github.com/users/DanHickstein/following{/other_user}","gists_url":"https://api.github.com/users/DanHickstein/gists{/gist_id}","starred_url":"https://api.github.com/users/DanHickstein/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/DanHickstein/subscriptions","organizations_url":"https://api.github.com/users/DanHickstein/orgs","repos_url":"https://api.github.com/users/DanHickstein/repos","events_url":"https://api.github.com/users/DanHickstein/events{/privacy}","received_events_url":"https://api.github.com/users/DanHickstein/received_events","type":"User","site_admin":false},"created_at":"2016-04-25T14:50:56Z","updated_at":"2016-04-25T14:50:56Z","body":"Great work @stggh, and thanks for all of the help @gerber-t!\r\n\r\nI am still a bit confused: If the betas are the coefficients for the functions, then shouldn't it be necessary to sum all of the betas in order to get the total \"intensity versus radius\" (speed distribution)?\r\n"}}