Hyperspectral Reconstruction using Discrete LED-Structured Illumination

We consider the use of digital signal processing to reconstruct continuous reflectance spectra using a small finite set of randomly illuminated light emitting diodes (LEDs). We simulate the use of LEDs having identical spectral distance and Gaussian bandwidth whose illumination overlaps its nearest neighbors. An object, whose reflectance spectrum is to be determined, is illuminated by a series of random spectral patterns consisting of randomly chosen LEDs with random intensity. We quantify the information within the illumination patterns using the singular value decomposition (SVD) and reconstruct reflectance spectra, specifically hemoglobin and several green vegetation spectra using the pseudoinverse of the SVD for a given amount of noise. We show that for sparse plant spectra, it is possible to reconstruct the continuous green vegetation spectra with RMSE less than 1% with as few as 25 LEDs. Our study demonstrates that reconstructing sparse reflectance spectra based on random structured illumination can enable low-cost LED-based cameras to perform equally well as expensive cameras, especially for dedicated applications.