Development of 3D Spectrometry using Compressive Sensing
Abstract: Multi-spectral imaging is a powerful approach in spectral analysis of objects with spatial details. However, such approaches are most often time consuming and experimentally complex since both spectral and spatial information in two dimensions are to be resolved. Presented here is an alternative approach to thee-dimensional spectroscopy, utilizing the Compressive Sensing methodology to treat a digital image as an underrepresented system of equations. By utilizing the properties of random bases and enforcing sparsity onto a spectral two-dimensional scene using a binary mask the system of equations can be solved numerically and thus allow spectral separation of two-dimensional spectral scenes in a post-processing script. To achieve this goal, an approach is presented in this report where 1) a spectrometer setup was modified and utilized, 2) an image analysis approach based on Compressive Sensing was developed 3) the method was employed and analyzed for a number of different data sets and 4) an objective measure of reconstruction quality of spectral components was created and evaluated. The outcome of this work clearly show that Compressive Imaging has potential to become a widely used tool in multispectral imaging and that it, despite some drawbacks, is a big step forwards from conventional three-dimensional spectrometry
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