Sparse Reconstruction Using Block Sparse Bayesian Learning With Fast Marginalized Likelihood Maximization for Near-Infrared Spectroscopy

Abstract

The absorption peak contains a great amount of important chemical information that is critical for the qualitative/quantitative analysis of organic compounds in high-dimensional near-infrared (NIR) spectral data. Sparse Bayesian learning (SBL) algorithm can capture key information from the underlying signal with only a small number of measurements. The computational cost is high because the inverse of a large matrix must be calculated in each iteration with the use of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula> -norm approximation or least squares. To overcome this problem, an improved block SBL (BSBL) is adopted to first reconstruct the absorption peak variables by determining the position and width of the limited peaks autonomously. Then, the fast-marginalized likelihood maximization (FMLM) is used to obtain the optimal hyperparameters of the cost function and realize a fast convergence rate. The proposed method is verified using two NIR spectral datasets and compared with the full-spectral-based partial least squares (PLS) and the other three models. The results demonstrate that the proposed method has a low computational cost without losing prediction performance for the NIR spectroscopy (NIRS).