Sparse Modeling for Spectrometer Based on Band Measurement

Kyoya Uemura, Tomoyuki Obuchi, Toshiyuki Tanaka

Abstract: In typical spectrometric measurement systems, a high-resolution spectrum is obtained directly via sequential observations with a narrow measurement window at the expense of sensitivity. In this paper, we design a class of simple multiplexed measurement with a wide measurement window, which we term Band Measurement (BM), to achieve high sensitivity. We then propose a multiplexed spectrometric method for sparse spectra, named BM-lasso, in which least absolute shrinkage and selection operator (lasso) is combined with BM to reconstruct an original high-resolution spectrum from the low-resolution measurement signals obtained by BM. BM has the significant practical advantage that it can be easily implemented in spectrometric measurement systems; hence device alterations or complex measurement systems are not required. BM also has the theoretical advantage of having the (high-order) Markov property to ease the theoretical analyses. To perform an analytical evaluation of the proposed method, we derive density evolution equations for belief propagation on the high-order Markov chain with nonGaussian state distribution and obtain the expected errors of estimators of BM-lasso. The result reveals that BM-lasso achieves a lower mean square error than the conventional method at any signal-to-noise ratio. Furthermore, simulation studies with both artificial and actual mass spectra show that BM-lasso significantly improves the accuracy, sensitivity, and specificity compared with the conventional method, demonstrating the practicality of the proposed method.