Efficient experimental sampling through low-rank matrix recovery

Abstract

Abstract Low-rank matrix recovery allows a low-rank matrix to be reconstructed when only a fraction of its elements is available. In this paper, an approximate Bayesian approach to low-rank matrix recovery is developed and its potential benefit for an application in metrology explored. The approach extends a recently proposed Bayesian low-rank matrix recovery procedure by utilizing a Gaussian Markov random field (GMRF) prior. The GMRF prior accounts for spatial smoothness, which is relevant for applications such as quantitative magnetic resonance imaging and nano Fourier transform infrared (FTIR) spectroscopy. The approach proposed here is automatic in that its hyperparameters are estimated from the data. Application to nano-FTIR spectroscopy demonstrates that the effort required to perform experiments in the time-consuming measurement of multi-dimensional data can be reduced significantly. Software for the proposed approach is available upon request.