{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T17:12:57Z","timestamp":1772298777568,"version":"3.50.1"},"reference-count":88,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2021,8,19]],"date-time":"2021-08-19T00:00:00Z","timestamp":1629331200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/S028730\/1"],"award-info":[{"award-number":["EP\/S028730\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Spectral reconstruction (SR) algorithms attempt to recover hyperspectral information from RGB camera responses. Recently, the most common metric for evaluating the performance of SR algorithms is the Mean Relative Absolute Error (MRAE)\u2014an \u21131 relative error (also known as percentage error). Unsurprisingly, the leading algorithms based on Deep Neural Networks (DNN) are trained and tested using the MRAE metric. In contrast, the much simpler regression-based methods (which actually can work tolerably well) are trained to optimize a generic Root Mean Square Error (RMSE) and then tested in MRAE. Another issue with the regression methods is\u2014because in SR the linear systems are large and ill-posed\u2014that they are necessarily solved using regularization. However, hitherto the regularization has been applied at a spectrum level, whereas in MRAE the errors are measured per wavelength (i.e., per spectral channel) and then averaged. The two aims of this paper are, first, to reformulate the simple regressions so that they minimize a relative error metric in training\u2014we formulate both \u21132 and \u21131 relative error variants where the latter is MRAE\u2014and, second, we adopt a per-channel regularization strategy. Together, our modifications to how the regressions are formulated and solved leads to up to a 14% increment in mean performance and up to 17% in worst-case performance (measured with MRAE). Importantly, our best result narrows the gap between the regression approaches and the leading DNN model to around 8% in mean accuracy.<\/jats:p>","DOI":"10.3390\/s21165586","type":"journal-article","created":{"date-parts":[[2021,8,19]],"date-time":"2021-08-19T09:58:06Z","timestamp":1629367086000},"page":"5586","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["On the Optimization of Regression-Based Spectral Reconstruction"],"prefix":"10.3390","volume":"21","author":[{"given":"Yi-Tun","family":"Lin","sequence":"first","affiliation":[{"name":"School of Computing Sciences, University of East Anglia, Norwich NR4 7TJ, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Graham D.","family":"Finlayson","sequence":"additional","affiliation":[{"name":"School of Computing Sciences, University of East Anglia, Norwich NR4 7TJ, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"480","DOI":"10.2352\/CGIV.2002.1.1.art00101","article-title":"On the spectral dimensionality of object colours","volume":"Volume 2002","author":"Hardeberg","year":"2002","journal-title":"Proceedings of the Conference on Colour in Graphics, Imaging, and Vision"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1007","DOI":"10.1364\/JOSAA.14.001007","article-title":"Linear bases for representation of natural and artificial illuminants","volume":"14","author":"Romero","year":"1997","journal-title":"J. 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